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  • 1
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 23 (1982), S. 326-340 
    ISSN: 1436-4646
    Schlagwort(e): Optimization ; Quasi-Newton ; Conjugate Gradient
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper we study conjugate gradient algorithms for large optimization problems. These methods accelerate (or precondition) the conjugate gradient method by means of quasi-Newton matrices, and are designed to utilize a variable amount of storage, depending on how much information is retained in the quasi-Newton matrices. We are concerned with the behaviour of such methods on the underlying quadratic model, and in particular, with finite termination properties.
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  • 2
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 19 (1980), S. 61-77 
    ISSN: 1436-4646
    Schlagwort(e): Optimization ; Nonlinear Programming ; Unconstrained Optimization ; Nondifferentiable Optimization ; Min—Max Problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract In this paper, we suggest approximations for smoothing out the kinks caused by the presence of “max” or “min” operators in many non-smooth optimization problems. We concentrate on the continuous-discrete min—max optimization problem. The new approximations replace the original problem in some neighborhoods of the kink points. These neighborhoods can be made arbitrarily small, thus leaving the original objective function unchanged at almost every point ofR n . Furthermore, the maximal possible difference between the optimal values of the approximate problem and the original one, is determined a priori by fixing the value of a single parameter. The approximations introduced preserve properties such as convexity and continuous differentiability provided that each function composing the original problem has the same properties. This enables the use of efficient gradient techniques in the solution process. Some numerical examples are presented.
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  • 3
    Digitale Medien
    Digitale Medien
    Springer
    Mathematical programming 47 (1990), S. 175-201 
    ISSN: 1436-4646
    Schlagwort(e): Optimization ; linear programming ; complexity ; polynomial time algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract We present an algorithm for linear programming which requires O(((m+n)n 2+(m+n)1.5 n)L) arithmetic operations wherem is the number of constraints, andn is the number of variables. Each operation is performed to a precision of O(L) bits.L is bounded by the number of bits in the input. The worst-case running time of the algorithm is better than that of Karmarkar's algorithm by a factor of $$\sqrt {m + n} $$ .
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  • 4
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 42 (1983), S. 147-154 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We give sufficient conditions for convergence of the chord method for a class of singular problems. The rate of convergence is sublinear.
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  • 5
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 175-193 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS) (1980) ; Primary 65J05, 65J15 ; Secondary 47H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary For solving a nonlinear operator equationF(x)=0 in Banach spaces, the Newton's method or Newton type methods are important numerical techniques. We use the properties of real equationt=Φ(t) majorizing an operator equationx=Gx to find a fixed point ofG as a solution of equationF(x)=0. Various type of operatorsG are considered in this paper. For a nonlinear operatorG, we would find a real function Φ majorizing the operatorG and it will be related to a rate of convergence $$\omega (r) = \frac{{r^2 }}{{2(r^2 + d)^{1/2} }}.$$ It follows thatG has a fixed point as a solution ofF(x)=0. Practical limitations of error bounds like as in Potra and Pták [5] are discribed.
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  • 6
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 325-340 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Beschreibung / Inhaltsverzeichnis: Summary In this paper we present convergence results for the asynchronous algorithms based essentially on the notion of classical contraction. We generalize, in particular, all convergence results for those algorithms which are based on the vectorial norm hypothesis, in wide spread use recently. Certain problems, for which the vectorial norm hypothesis can be difficult or even impossible to verify, can nontheless be tackled within the scope of the classical contraction that we adopte.
    Notizen: Resumé Nous présentons dans cet article des résultats de convergence des algorithmes asynchrones basés essentiellement sur la notion classique de contraction. Nous généralisons, en particulier, tous les résultats de convergence de ces algorithmes qui font l'hypothèse de contraction en norme vectorielle qui récemment a été très souvant utilisée. Par ailleurs, l'hypothèse de contraction en norme vectorielle peut se trouver difficile, voire impossible à vérifier pour certains problèmes qui peuvent être cependant abordés dans le cadre de la contraction classique que nous adoptons.
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  • 7
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 39 (1982), S. 429-448 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper considers local convergence properties of inexact partitioned quasi-Newton algorithms for the solution of certain non-linear equations and, in particular, the optimization of partially separable objective functions. Using the bounded deterioration principle, one obtains local and linear convergence, which impliesQ-superlinear convergence under the usual conditions on the quasi-Newton updates. For the optimization case, these conditions are shown to be satisfied by any sequence of updates within the convex Broyden class, even if some Hessians are singular at the minimizer. Finally, local andQ-superlinear convergence is established for an inexact partitioned variable metric method under mild assumptions on the initial Hessian approximations.
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  • 8
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 111-117 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary We seek an approximation to a zero of a continuous functionf:[a,b]→ℝ such thatf(a)≦0 andf(b)≧0. It is known that the bisection algorithm makes optimal use ofn function evaluations, i.e., yields the minimal error which is (b−a)/2 n+1, see e.g. Kung [2]. Traub and Wozniakowski [5] proposed using more general information onf by permitting the adaptive evaluations ofn arbitrary linear functionals. They conjectured [5, p. 170] that the bisection algorithm remains optimal even if these general evaluations are permitted. This paper affirmatively proves this conjecture. In fact we prove optimality of the bisection algorithm even assuming thatf is infinitely many times differentiable on [a, b] and has exactly one simple zero.
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  • 9
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 42 (1983), S. 323-329 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A Newton-like iteration scheme is proposed for the tracing of an implicitly defined smooth curve. This scheme originates from the study of the continuous Newton-Raphson method for underdetermined systems and, hence, inherits the characteristic property of orthogonality. Its domain of attraction is formed and makes it possible to trace this curve more efficiently.
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  • 10
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 35 (1980), S. 223-230 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A generalized conjugate gradient algorithm which is invariant to a nonlinear scaling of a strictly convex quadratic function is described, which terminates after at mostn steps when applied to scaled quadratic functionsf: R n →R1 of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andh∈C 1 (R1) an arbitrary strictly monotone functionh. The algorithm does not suppose the knowledge ofh orF but only off(x) and its gradientg(x).
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  • 11
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 35 (1980), S. 293-313 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS) ; 90C30 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper considers a class of variable metric methods for unconstrained minimization. Without requiring exact line searches each algorithm in this class converges globally and superlinearly on convex functions. Various results on the rate of the superlinear convergence are obtained.
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  • 12
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 40 (1982), S. 93-98 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65D15 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Der Quotienten-Differenzen-Algorithmus nach Rutishauser ist geeignet zur Bestimmung von Polen meromorpher Funktionen, gegeben durch eine Taylorreihe. Sind mehrere Pole betragsgleich, so kann eine Polynomfolge bestimmt werden, deren Grenzpolynom diese Pole als Nullstellen hat. Die Konvergenz wurde von Rutishauser jedoch nicht bewiesen. Ein Beweis wird in der vorliegenden Arbeit präsentiert.
    Notizen: Summary The Quotient-Difference Algorithm of Rutishauser can be used for the determination of poles of a meromorphic function given by its power series. If some of the poles have same modulus, a sequence of polynomials can be determined such that the limiting polynomial has exactly these poles as zeros. The convergence has not been proved by Rutishauser, however. A proof is presented in this paper.
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  • 13
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 42 (1983), S. 31-50 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65J10 ; 41A25 ; 41A65 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Error bounds are given for the iterative computation of the eigenvectors in the Rayleigh-Schrödinger series. These bounds remove the discrepancy in the theoretical behaviour and numerical results, noted by Redont, under the assumption of collectively compact convergence. As a particular case, it follows that the eigenvector in the iterative Galerkin method proposed by Sloan improves upon the eigenvector in the Galerkin method. This is illustrated by numerical experiments.
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  • 14
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 42 (1983), S. 97-105 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Generalized conjugate gradient algorithms which are invariant to a nonlinear scaling of a strictly convex quadratic function are described. The algorithms when applied to scaled quadratic functionsf∶R n →R 1 of the formf(x)=h(F(x)) withF(x) strictly convex quadratic andh∈C 1(R 1) an arbitrary strictly monotone functionh generate the same direction vectors as for the functionF without perfect steps.
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  • 15
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 34 (1980), S. 63-72 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The method of nondiscrete mathematical induction is applied to the Newton process. The method yields a very simple proof of the convergence and sharp apriori estimates; it also gives aposteriori bounds which are, in general, better than those given in [1].
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  • 16
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 34 (1980), S. 73-85 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65K05 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The theoretical convergence of Generalized Reduced Gradient Method (GRG) has not been proved; the purpose of this paper is to propose two theoritical and general variants of the original method and a proof of their convergence.
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  • 17
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 34 (1980), S. 411-429 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65N10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The inverse Stefan problem can be understood as a problem of nonlinear approximation theory which we solved numerically by a generalized Gauss-Newton method introduced by Osborne and Watson [19]. Under some assumptions on the parameter space we prove its quadratic convergence and demonstrate its high efficiency by three numerical examples.
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  • 18
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 35 (1980), S. 95-111 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Given a solutionx * of a system of nonlinear equationsf with singular Jacobian ∇f(x *) we construct an open starlike domainR of initial points, from which Newton's method converges linearly tox *. Under certain conditions the union of those straight lines throughx *, that do not intersect withR is shown to form a closed set of measure zero, which is necessarily disjoint from any starlike domain of convergence. The results apply to first and higher order singularities.
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  • 19
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 383-392 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Recently an iterative method for the solution of systems of nonlinear equations having at leastR-order 1+ $$\sqrt 2 $$ for simple roots has been investigated by the author [7]; this method uses as many function evaluations per step as the classical Newton method. In the present note we deal with several properties of the method such as monotone convergence, asymptotic inclusion of the solution and convergence in the case of multiple roots.
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  • 20
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 393-416 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 49D05, 49D07, 65K10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A method for approximating the optimal control and the optimal state for a class of distributed control problems governed by variational inequalities is given. It uses a Rayleigh-Ritz-Galerkin scheme, regularising techniques and a gradient algorithm. A numerical example is given.
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  • 21
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 427-445 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS) 65J15, 65G99 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary Sharp a priori and a posteriori error bounds are given for the secant method for solving non-linear equations in Banach spaces. The numerical stability of this method is also investigated. The stability results are analogous to those obtained by Lancaster for Newton's method.
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  • 22
    Digitale Medien
    Digitale Medien
    Springer
    Numerische Mathematik 38 (1982), S. 455-465 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10, 47H17 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary A numerical technique is described for computing turning points of a space curveL implicitly defined by a nonlinear system ofn equations inn+1 variables. The basic idea is a local parametrization ofL where the parameter that gives the next iterate is determined by applying one step of the well-known method for minimizing a real function using cubic Hermite interpolation with two nodes. The method is shown to convergeQ-super-linearly and withR-order of at least two. A numerical example concerning the analysis of nonlinear resistive circuits shows the algorithm to work effectively on real life problems.
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  • 23
    Digitale Medien
    Digitale Medien
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    Numerische Mathematik 36 (1980), S. 333-346 
    ISSN: 0945-3245
    Schlagwort(e): AMS (MOS) ; 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary The method of nondiscrete mathematical induction is applied to a multistep variant of the secant method. Optimal conditions for convergence as well as error estimates, sharp in every step, are obtained.
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  • 24
    Digitale Medien
    Digitale Medien
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    Numerische Mathematik 39 (1982), S. 119-137 
    ISSN: 0945-3245
    Schlagwort(e): AMS(MOS): 65H10 ; CR: 5.15
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Summary This paper presents a minimization method based on the idea of partitioned updating of the Hessian matrix in the case where the objective function can be decomposed in a sum of convex “element” functions. This situation occurs in a large class of practical problems including nonlinear finite elements calculations. Some theoretical and algorithmic properties of the update are discussed and encouraging numerical results are presented.
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  • 25
    Digitale Medien
    Digitale Medien
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    Mathematical geology 22 (1990), S. 107-121 
    ISSN: 1573-8868
    Schlagwort(e): Variogram ; geostatistics ; sample support ; variance
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The effect of sample support size on variance is examined and evaluated. Results based on variograms and geostatistics are compared to the classical relationship developed by H. F. Smith in 1938; that is, that the variance is reduced fromV 1 toV 1 /n b as the support area increases from I ton plots for uniformity trials. The exponentb is between zero and one. Theoretical results are based on use of auxiliary functions and account for the size and shape of the sample support and the overall field geometry. Results are given in terms of approximations by rational functions for ease of calculation. Experimental results for uniformity trials, infiltration measurements, and spectral data from satellites are compared to theoretical and empirical results. Applications include not only uniformity trials, but also measurement theory.
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  • 26
    Digitale Medien
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    Mathematical geology 22 (1990), S. 123-144 
    ISSN: 1573-8868
    Schlagwort(e): nonlinear estimators ; geostatistics ; confidence intervals ; indicator kriging ; probability kriging ; disjunctive kriging
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Approximate local confidence intervals can be produced by nonlinear methods designed to estimate indicator variables. The most precise of these methods, the conditional expectation, can only be used in practice in the multi-Gaussian context. Theoretically, less efficient methods have to be used in more general cases. The methods considered here are indicator kriging, probability kriging (indicator-rank co-kriging), and disjunctive kriging (indicator co-kriging). The properties of these estimators are studied in this paper in the multi-Gaussian context, for this allows a more detailed study than under more general models. Conditional distribution approximation is first studied. Exact results are given for mean squared errors and conditional bias. Then conditional quantile estimators are compared empirically. Finally, confidence intervals are compared from the points of view of bias and precision.
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  • 27
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    Mathematical geology 22 (1990), S. 573-588 
    ISSN: 1573-8868
    Schlagwort(e): classification ; regionalization ; Bayes' theorem ; geostatistics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The concept of multivariate classification of “geological objects” can be combined with the concept of regionalized variables to yield a procedure for typification of geological objects, such as rock units, well records, or samples. Numerical classification is followed by subdivision of the area of investigation, and culminates in a regionalization or mapping of the classification onto the plane. Regions are subdivisions of the map area which are spatially contiguous and relatively homogeneous in their geological properties. The probability of correct classification of each point within a region as being part of that region can be assessed in terms of Bayesian probability as a space-dependent function. The procedure is applied to subsurface data from western Kansas. The geologic properties used are quantitative variables, and relationships are expressed by Mahalanobis' distances. These functions could be replaced by other metrics if qualitative or binary data derived from geological descriptions or appraisals were included in the analysis.
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  • 28
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    Mathematical geology 22 (1990), S. 611-623 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; geohydrology ; kriging ; spatiotemporal variables
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Spatiotemporal variables constitute a large class of geohydrological phenomena. Estimation of these variables requires the extension of geostatistical tools into the space-time domain. Before applying these techniques to space-time data, a number of important problems must be addressed. These problems can be grouped into four general categories: (1) fundamental differences with respect to spatial problems, (2) data characteristics, (3) structural analysis including valid models, and (4) space-time kriging. Adequate consideration of these problems leads to more appropriate estimation techniques for spatiotemporal data.
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  • 29
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    Mathematical geology 22 (1990), S. 763-777 
    ISSN: 1573-8868
    Schlagwort(e): spatial estimation ; entropy ; Bayes law ; information ; geostatistics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The purpose of this paper is to stress the importance of a Bayesian/maximum-entropy view toward the spatial estimation problem. According to this view, the estimation equations emerge through a process that balances two requirements: High prior information about the spatial variability and high posterior probability about the estimated map. The first requirement uses a variety of sources of prior information and involves the maximization of an entropy function. The second requirement leads to the maximization of a so-called Bayes function. Certain fundamental results and attractive features of the proposed approach in the context of the random field theory are discussed, and a systematic spatial estimation scheme is presented. The latter satisfies a variety of useful properties beyond those implied by the traditional stochastic estimation methods.
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  • 30
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    Mathematical geology 12 (1980), S. 285-303 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; lognormal distribution ; mine planning ; ore reserve estimation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract When planning highly selective mining operations, the challenge is to estimate mineable ore reserves that will be selected at the mining stage. From exploration data it is not possible to estimate accurately the grade (or thickness) of each future selective mining unit; however, it is possible to estimate the local distributions of these mining unit grades within large panels suitable for long-range mine planning. Application of a cut-off then allows estimation of the recovered ore tonnage and grade within each such panel. Derivation of local conditional distributions is rather simple when the grade is either normally or lognormally distributed. The geologically important lognormal case is fully described both in the stationary and the nonstationary case. Cross validations of these techniques using the exploration data of the Imouraren uranium deposit are presented.
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  • 31
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    Mathematical geology 12 (1980), S. 25-32 
    ISSN: 1573-8868
    Schlagwort(e): random function ; geostatistics ; simulation ; covariance
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract This paper presents a new geostatistical method to obtain realizations of stationary random functions in the plane.
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  • 32
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    Mathematical geology 12 (1980), S. 305-320 
    ISSN: 1573-8868
    Schlagwort(e): disjunctive kriging ; logarithmic kriging ; gold evaluation ; geostatistics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The method of disjunctive kriging is applied to the evaluation of blocks of ore in a gold mine, and the estimated block values are compared with the true block values. First the theory of disjunctive kriging as applicable to mine valuation is presented from the user's viewpoint. The theory is then applied to process sample values originating from a large gold mine. Using the computer simulation of a number of sampling programs, estimated values and true values are compared. The disjunctive kriging estimates are also compared with estimates obtained by other methods of evaluation, including logarithmic kriging. It is shown that the results obtained, using real world data, are in complete agreement with the results expected according to the geostatistical theory.
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  • 33
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    Mathematical geology 12 (1980), S. 321-337 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; kriging ; variogram analysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The Nanisivik Pb-Zn deposit at Strathcona Sound, northern Baffin Island, Canada, is an orebody that is an S-shaped lens 3000 m long, 75 m wide, and 2–20 m thick. It is an epigenetic karst channel filling. Total reserves are 6.9 million short tons of 14.12% Zn, 1.4% Pb, and 1.77 oz of Ag per ton. The mine was brought into production in 1976 at a rate of 2000 short tons per day. In the preproduction phase variogram studies based only on surface holes indicated a random distribution. For the evaluation of grades and for the determination of the confidence limits, classic statistical procedures were applied. Since the drilling density was different in different ore zones, a model was developed to test the effect of different drill hole spacings on the uncertainties in the present value in a discounted cash flow model. After the initial development and mining stage, structures could be recognized in semivariograms. Studies for a best drilling grid showed that the pattern of 25 ×20 m used in the mine could be extended to 35 ×35 m, taking into account that eight stopes are mined simultaneously. For ore reserve calculations weighing factors were calculated by kriging for six universally applicable geometric situations. Only the drill holes within a block and immediately surrounding it were taken into account. A test in a well-known zone yielded satisfactory results. A test to predict highs and lows of the grade accurately enough to optimally place the pillars failed.
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  • 34
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    Mathematical geology 14 (1982), S. 309-319 
    ISSN: 1573-8868
    Schlagwort(e): Bias ; drift ; semivariogram ; geostatistics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract When nonlinear drift is present, the nature of the bias in the experimental semivariogram estimator of the semivariogram function is determined by the extent and density of the sampling as well as by the drift function itself. The bias caused by drift may affect the interpretation of the experimental semivariogram over its entire range.
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  • 35
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    Mathematical geology 14 (1982), S. 645-660 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; uranium ; production forecast
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Geostatistical estimation techniques were customized to allow forecasting of production figures at the Silver Bell uranium mine (Uravan District).Surface drill hole data were used to provide a block model of kriged estimators of average uranium grades. Figures for recoverable ore grade and the ore-waste ratio are then deduced from regressive curves previously obtained from underground information and production data. Cross-validations of the entire model were performed and were found positive.
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  • 36
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    Mathematical geology 14 (1982), S. 87-106 
    ISSN: 1573-8868
    Schlagwort(e): coal ; geostatistics ; kriging ; regional estimation ; systematic sampling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Two-dimensional systematic sampling of small plots followed by the kriging of those plots may be employed to obtain regional estimates of coal resources and measures of the accuracy of the estimates. The use of sampling makes large savings in computation possible. Two case studies involving the estimation of coal tonnage are discussed.
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  • 37
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    Mathematical geology 15 (1983), S. 445-468 
    ISSN: 1573-8868
    Schlagwort(e): indicator kriging ; geostatistics ; nonparametric
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The indicator approach, whereby the data are used through their rank order, allows a nonparametric approach to the data bivariate distribution. Such rich structural information allows a nonparametric risk-qualified, estimation of local and global spatial distributions.
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  • 38
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    Mathematical geology 15 (1983), S. 259-286 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; local recovery ; conditional expectation ; multigaussian kriging ; disjunctive kriging
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The performance of the geostatistical techniques of disjunctive kriging and multigaussian kriging for the estimation of local recovered reserves are compared using a simulated deposit.
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  • 39
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    Mathematical geology 15 (1983), S. 517-536 
    ISSN: 1573-8868
    Schlagwort(e): Kriging ; geostatistics ; regression effect
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract One traditional method of estimating ore reserves is to allocate the arithmetic mean of local samples to each block or stope within the deposit. Thirty years ago, Krige showed that this method produced a “bias” in the estimates, in that high values were commonly overestimated and low values underestimated. This bias became known as the “regression effect” because it could usually be corrected by an empirical regression relationship derived from previously mined areas. This paper shows how the regression effect can be reconciled with the geostatistical method of kriging and how a simple regression line may be derived before any areas are mined out. The method is similar to kriging with known mean, but acknowledges that the overall mean of the deposit may not be known precisely.
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  • 40
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    Mathematical geology 12 (1980), S. 577-588 
    ISSN: 1573-8868
    Schlagwort(e): variogram ; geostatistics ; estimation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The application of regionalized variables requires the estimation of the variogram function and the evaluation of its integral. By representing the variogram by a polygonal function the integral may be easily approximated by closed form representations of polygonal integrals. This approach provides a basis for more extensive statistical evaluation not evident in existing approximation methods. This paper provides the closed form representations for two-dimensional variogram functions whose domain is represented by a finite collection of rectangles.
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  • 41
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    Mathematical geology 14 (1982), S. 57-64 
    ISSN: 1573-8868
    Schlagwort(e): estimation ; generalized covariance function ; generalized increments ; geostatistics ; intrinsic random functions ; multicollinearity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The estimation of the generalized covariance function, K, is a major problem in the use of intrinsic random functions of order k to obtain kriging estimates. The precise estimation by least-squares regression of the parameters in polynomial models for K is made difficult by the nature of the distribution of the dependent variable and the multicollinearity of the independent variables.
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  • 42
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    Mathematical geology 14 (1982), S. 557-564 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; variogram ; outliers
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Variograms for gold and lead values from the Loraine and Prieska mines, respectively, indicate that data outliers can seriously distort and/or mask the real variogram patterns. Studies show that this problem is best overcome for these mines by logarithmic transformation of the data, and/or a suitable screening out of such outliers, and/or more robust variogram estimation procedures; the benefits are particularly significant when the basic data is limited.
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  • 43
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    Mathematical geology 14 (1982), S. 217-239 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; variograms ; anisotropies ; tungsten
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The regionalization of tungsten grades at the χ deposit represents an ideal case for anisotropic hole-effect variogram modeling. The modeling technique is presented step by step and the consequences of the model on block kriging are indicated.
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  • 44
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    Mathematical geology 14 (1982), S. 387-404 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; resource estimation ; geoexploration ; sampling
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Sampling exploration of uncertain functions to locate critical contour levels is most effective if sampling decisions are made sequentially. A simple sequential exploration strategy, based on pseudo-Bayesian second-moment analysis, is proposed and compared with non-sequential systematic sampling. Repeated application to functions simulated pseudorandomly from stationary random processes on the line and on the plane indicates uniform superiority of the sequential strategy. The method is particularly advantageous when the function of interest,h(X), has an uncertain trend, and in general when the random process that quantifies prior uncertainty onh(X) is highly correlated.
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  • 45
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    Mathematical geology 14 (1982), S. 547-555 
    ISSN: 1573-8868
    Schlagwort(e): geostatistics ; kriging
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Parallel variogram analyses, block kriging, and follow-up studies were effected for the lead content of part of the Prieska copper-zinc ore body and for the gold content of the highly variable Breef in a section of the Loraine gold mine, based first on untransformed values and second on logarithmically transformed values using the lognormal-de Wijsian model. For both models the effect was also analyzed of using the population mean or ignoring it. Practical follow-up comparisons confirm theoretical considerations and show that on these mines conditional biases can be eliminated conveniently by kriging with mean; also that the lognormal-de Wijsian model with mean gives the best results.
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  • 46
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    Mathematical geology 15 (1983), S. 183-195 
    ISSN: 1573-8868
    Schlagwort(e): Computers ; data files ; exploration ; geostatistics ; petroleum ; prospects ; spatial filtering ; trend analysis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract Computer recognition of prospective areas through the processing of digital exploration data can be effective if the statistical tests for the determination of the prospects are pertinent to the presence of the desired mineral. Where exploration involves the application of polynomial trend analysis to structure contour maps in the search for petroleum and natural gas, standard analysis of variance tests may not indicate the best exploration maps. Variance tests may be completely invalid where isolated dips and clustered samples cause the surfaces generated by some of the most common trend programs to oscillate, creating a false impression of variance. On the other hand, tests that directly compare the position of residual features with areas of known production consistently indicate the best map for the determination of new prospects. They are simple to apply and appear to offer the most opportunity for the automatic recognition of prospective areas.
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  • 47
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    Mathematical geology 22 (1990), S. 915-932 
    ISSN: 1573-8868
    Schlagwort(e): sample design ; geostatistics ; spatial classification
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Geologie und Paläontologie , Mathematik
    Notizen: Abstract The criterion used to select infill sample locations should depend on the sampling objective. Minimizing the global estimation variance is the most widely used criterion and is suitable for many problems. However, when the objective of the sampling program is to partition an area of interest into zones of high values and zones of low values, minimizing the expected cost of classification errors is a more appropriate criterion. Unlike the global estimation variance, the cost of classification errors incorporates both the sample locations and the sample values into an objective infill-sampling design criterion.
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  • 48
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    Journal of optimization theory and applications 36 (1982), S. 495-519 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; nonlinear programming ; Numerical methods ; computational methods ; augmented Lagrangian functions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, a new augmented Lagrangian function is introduced for solving nonlinear programming problems with inequality constraints. The relevant feature of the proposed approach is that, under suitable assumptions, it enables one to obtain the solution of the constrained problem by a single unconstrained minimization of a continuously differentiable function, so that standard unconstrained minimization techniques can be employed. Numerical examples are reported.
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  • 49
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    Journal of optimization theory and applications 38 (1982), S. 25-31 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; Kuhn-Tucker theorem ; LegendreK-transform ; equilibrium composition
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The most common way of determining the steady states of a system is through the optimization of a concave function on a convex set. This applies only to cases where the objective function depends exclusively onextensive variables. In fields such as econometrics, physics, or chemistry, controllable quantities (and therefore constrained variables) are generally referred to asintensive parameters, and the states are described through a potential function. In the following pages, we examine how these two aspects can be connected.
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  • 50
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    Journal of optimization theory and applications 38 (1982), S. 409-422 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; scalar optimization ; vector optimization ; optimization under vector-valued criteria ; maximum principle ; dynamic programming ; optimization of dynamic systems ; multi-criteria decision problems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The optimal control problem with vector-valued criteria is considered. A new approach to the generalization of this problem and a method of constructing the Bellman function are given.
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  • 51
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    Journal of optimization theory and applications 39 (1983), S. 89-104 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; optimal strategies ; value of a game ; terminal cost function
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A two-person, zero-sum differential game with general type phase constraints and terminal (not fixed) cost function is investigated. Player II (possessing complete information) can choose any strategy in the Varaiya-Lin sense, while his opponent (having incomplete information) can select any lower II-strategy introduced by Friedman (Ref. 1). The existence of a value and an optimal player II's strategy is obtained under assumptions ensuring that the sets of all admissible trajectories for the two players are compact in the Banach space of all continuous functions. The present paper largely extends the results of Ref. 2.
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  • 52
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    Journal of optimization theory and applications 31 (1980), S. 553-564 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; perturbation theory ; systems order reduction ; large-scale systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract For interconnected systems with slow and fast modes, we analyze a multimodel design of a Nash equilibrium strategy. Decision makers use different models of the same system to obtain a composite strategy that approximates the exact Nash strategy. It is discussed in what sense this approximation holds.
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  • 53
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    Journal of optimization theory and applications 32 (1980), S. 365-377 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; pursuit and evasion ; capture avoidance ; linear games
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We formulate the problems of capture and avoidance as differential games with terminal cost, thus avoiding some difficulties arising from choosing the terminal time or the closest distance as the cost. This puts capture and avoidance in the context of differential games, in the sense of Isaacs. The results are illustrated via linear differential games with hard control constraints.
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  • 54
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    Journal of optimization theory and applications 32 (1980), S. 463-478 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; control ; relativity ; stochastic processes ; wave mechanics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The intention of this paper is to show how the influence of the work of Bellman has initiated a tentative new approach to quantum mechanics
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  • 55
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    Journal of optimization theory and applications 40 (1983), S. 595-623 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; partial differential equations ; elasticity ; control ; design sensitivity
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The dependence of the static response and the eigenvalues of a membrane on its shape is characterized. A transformation function is defined to determine the shape of the membrane. Differential operator properties and transformation techniques of integral calculus are employed to show that the static response and the eigenvalues of the system depend in a continuous and differentiable way on the shape of the membrane. Explicit and computable formulas are presented for the derivative (first variation) of the structural response and the eigenvalues with respect to the shape. A rigorous proof is provided, and the shape design sensitivity of a typical integral functional is determined.
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  • 56
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    Journal of optimization theory and applications 41 (1983), S. 587-598 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; first reachability of sets ; playability ; pursuit-evasion problem
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider a qualitative differential game between two players, each with their own respective target. A player's objective is to steer the response of a dynamical system under the control of both players into his own target before his opponent can steer it to his. The sufficiency conditions given by Getz and Leitmann (Ref. 2), which ensure termination on a particular target, are improved. The theory is illustrated by a pursuit-evasion problem.
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  • 57
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    Mathematical methods of operations research 34 (1990), S. 43-58 
    ISSN: 1432-5217
    Schlagwort(e): Linear Search ; Optimization ; Absolutely Continuous distributions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Beschreibung / Inhaltsverzeichnis: Zusammenfassung Ein Objekt, das sich in zufälliger Position auf einer Strecke befindet, soll gesucht werden; der Startpunkt liegt im Inneren der Strecke. Für die Bewegungsgeschwindigkeit bei der Suche ist eine obere Schranke gegeben; der Suchpfad muß stetig sein, wobei beliebig viele Richtungsänderungen zugelassen sind. Das Ziel ist die Minimierung der erwarteten Zeit bis zum Erreichen des Objekts. Unter der Voraussetzung einer absolut stetigen Verteilung für die Position des Objekts werden hinreichende Bedingungen für die Optimalität eines Suchpfades angegeben.
    Notizen: Abstract The linear search problem is concerned with the search for a target located randomly on a line. The target being sought for might be on either side of some starting point. A searcher makes for the target with an upper bound on his speed, using a continuous search path in which he changes his direction many times before reaching his goal. The minimality of average distance (time) from the starting point upon reaching the target is the measure of optimality of search paths. We have obtained sufficient conditions that guarantee the minimality of such search paths whenever the target has an absolutely continuous distribution.
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  • 58
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    Journal of optimization theory and applications 37 (1982), S. 115-119 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; isochronous capture ; stroboscopic strategy
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In Ref. 1, Hájek formulated the conjecture that isochronous capture is necessarily stroboscopic in linear differential games. Here, it is shown that this conjecture is not valid.
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  • 59
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    Journal of optimization theory and applications 40 (1983), S. 321-331 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; necessary conditions ; Kuhn-Tucker theorem ; multiplier rules ; separation of convex sets ; mathematical programming ; generalized derivatives
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider the following abstract mathematical programming problem: in a setD, find an element that optimizes a real function φ0, subject to inequality constraints φ1⩽0, ..., φ p ⩽0 and equality constraints φ p+1=0, ..., φ p+q =0. Necessary conditions for this problem, like the Karush-Kuhn-Tucker theorem, can be seen as a consequence of separating with a hyperplane two convex sets inR p+q+1, the image space of the map Φ=(φ0, φ1, ..., φ p+q ). This paper reviews this approach and organizes it into a coherent way of looking at necessary conditions in optimization theory.
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  • 60
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    Journal of optimization theory and applications 36 (1982), S. 253-262 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; Nash equilibria ; open-loop strategies ; closed-loop strategies
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract It is well known that, in general, Nash equilibria in open-loop strategies do not coincide with those in closed-loop strategies. This note identifies a class of differential games in which the Nash equilibrium in closed-loop strategies is degenerate, in the sense that it depends on time only. Consequently, the closed-loop equilibrium is also an equilibrium in open-loop strategies.
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  • 61
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    Journal of optimization theory and applications 37 (1982), S. 315-341 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; unconstrained minimization ; updates ; line searches ; convergence ; numerical methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider a certain generalization of the Huang family of updates and discuss, firstly, convergence, dependence on parameters, and descent property; secondly, invariance under nonlinear scaling, conjugacy of search directions, and possibility of achieving a better approximation of the inverse of the Hessian. The last three aspects are shown to be dependent on particular choices of parameters. A numerical experiment is presented comparing the performances of the usual and modified BFGS algorithms.
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  • 62
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    Journal of optimization theory and applications 65 (1990), S. 501-518 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; value function ; programmed maximin function ; dispersal surface ; focal surface
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, the game of the optimal approach of two identical inertial pursuers to a noninertial evader is investigated. The duration of the game is fixed. The payoff functional is the distance between the evader and the closest pursuer when the game terminates. The value function is constructed for all possible positions of the game. The regions where the pursuit is one-to-one and the regions where it is essentially collective are described algorithmically. Some analogies between this game and the linear differential game with elliptical vectograms are indicated. It is noted that the focal surface and the dispersal surface are in proximity of one another.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 63
    Digitale Medien
    Digitale Medien
    Springer
    Journal of optimization theory and applications 37 (1982), S. 69-87 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; singular arcs ; saddle points ; two-point boundary-value problems ; switching times ; closed-loop solutions ; inverse systems
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract This paper develops a numerical technique to solve a class of zero-sum differential games with singular control. By using this technique and the application of inverse systems, a near-optimal closed-loop technique is developed to generate a numerical solution to this class of problems.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 64
    Digitale Medien
    Digitale Medien
    Springer
    Journal of optimization theory and applications 37 (1982), S. 121-122 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; pursuit and evasion ; captureavoidance ; linear games
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Corrections to some results of Ref. 1 are stated.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 65
    Digitale Medien
    Digitale Medien
    Springer
    Journal of optimization theory and applications 38 (1982), S. 581-598 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; optimal strategies ; value of a game
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A differential game of prescribed duration with general-type phase constraints is investigated. The existence of a value in the Varaiya-Lin sense and an optimal strategy for one of the players is obtained under assumptions ensuring that the sets of all admissible trajectories for the two players are compact in the Banach space of all continuous functions. These results are next widened on more general games, examined earlier by Varaiya.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 66
    Digitale Medien
    Digitale Medien
    Springer
    Journal of optimization theory and applications 64 (1990), S. 293-310 
    ISSN: 1573-2878
    Schlagwort(e): Differential games ; feedback Nash equilibria ; renewable resources ; common-property fishery
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The paper deals with a problem of optimal management of a common-property fishery, modelled as a two-player differential game. Under nonclassical assumptions on harvest rates and utilities, a feedback Nash equilibrium is determined, using a bionomic equilibrium concept. Later on, this assumption is relaxed and a feedback Nash equilibrium is established under minimal hypotheses.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 67
    Digitale Medien
    Digitale Medien
    Springer
    Journal of optimization theory and applications 64 (1990), S. 331-347 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; learning systems ; nonconvex programming ; process synthesis
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Optimization techniques are finding increasingly numerous applications in process design, in parallel to the increase of computer sophistication. The process synthesis problem can be stated as a largescale constrained optimization problem involving numerous local optima and presenting a nonlinear and nonconvex character. To solve this kind of problem, the classical optimization methods can lead to analytical and numerical difficulties. This paper describes the feasibility of an optimization technique based on learning systems which can take into consideration all the prior information concerning the process to be optimized and improve their behavior with time. This information generally occurs in a very complex analytical, empirical, or know-how form. Computer simulations related to chemical engineering problems (benzene chlorination, distillation sequence) and numerical examples are presented. The results illustrate both the performance and the implementation simplicity of this method.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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  • 68
    Digitale Medien
    Digitale Medien
    Springer
    Journal of optimization theory and applications 65 (1990), S. 305-319 
    ISSN: 1573-2878
    Schlagwort(e): Optimization ; shunt capacitors ; distribution feeders ; control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Loads on electric utility systems have two components: active power (measured in kilowatts) and reactive power (measured in kilovars). Active power has to be generated at the power plant, whereas reactive power can be provided by either power plants or capacitors. It is a well-known fact that shunt power capacitors are the most economical source to meet the reactive power requirements of inductive loads and transmission lines operating at a lagging power factor. This paper describes new contributions to the problem of optimization of size and control setting of shunt capacitors on distribution feeders, so that the losses along the feeder are minimized. The variation of the KVAR of the load on the feeder with the distance from the substation is assumed to be linear. The parameters of this function are estimated from the available KVAR loading on the feeder first by using least-square techniques and then by using least-absolute-value parameter estimation techniques. The results obtained are compared with that obtained if the current profile is assumed to be uniformly distributed on the feeder. Our results show that the optimum size of the capacitor bank as well as its optimum location depend on the parameters of the model used for the load. Also, our results show a large saving in the size of the capacitor banks used with a considerable per-unit-loss reduction along the feeder.
    Materialart: Digitale Medien
    Standort Signatur Erwartet Verfügbarkeit
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