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  • AMS(MOS): 65H10
  • Optimization
  • optimal control
  • Springer  (19)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
  • Elsevier
  • Wiley
  • 2005-2009
  • 1990-1994
  • 1980-1984  (19)
  • 2008
  • 1982  (19)
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Schlagwörter
Verlag/Herausgeber
  • Springer  (19)
  • American Chemical Society
  • Annual Reviews
  • Blackwell Publishing Ltd
  • Elsevier
    • +
Erscheinungszeitraum
  • 2005-2009
  • 1990-1994
  • 1980-1984  (19)
Jahr
  • 1
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    Digitale Medien
    Conjugate direction methods with variable storage (1982)
    Springer
    Mathematical programming 23 (1982), S. 326-340 
    Details
    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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01583797
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  • 2
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    Some convergence results for asynchronous algorithms (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 325-340 
    Details
    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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    URL: http://dx.doi.org/10.1007/BF01407866
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  • 3
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    Bisection is optimal (1982)
    Springer
    Numerische Mathematik 40 (1982), S. 111-117 
    Details
    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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01459080
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  • 4
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    Some supplementary results on the 1+ $$\sqrt 2 $$ order method for the solution of nonlinear equations (1982)
    Springer
    Numerische Mathematik 38 (1982), S. 383-392 
    Details
    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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01396439
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  • 5
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    Digitale Medien
    Partitioned variable metric updates for large structured optimization problems (1982)
    Springer
    Numerische Mathematik 39 (1982), S. 119-137 
    Details
    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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01399316
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  • 6
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    A new augmented Lagrangian function for inequality constraints in nonlinear programming problems (1982)
    Springer
    Journal of optimization theory and applications 36 (1982), S. 495-519 
    Details
    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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00940544
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  • 7
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    Minimum-time 180° turns of aircraft (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 83-96 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Numerical methods ; multiple shooting method ; optimal control ; aircraft trajectories ; flight mechanics
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Three-dimensional minimum-time 180° turns of a fighter aircraft are computed for several initial velocitiesV 0 and altitudesh 0. It is shown that the optimum turns consist of split -S maneuvers forV 0≦V 10, three-dimensional maneuvers forV 10〈V 0〈V 20, and half-loops forV 0≧V 20, withV 10,V 20 being functions of altitude or thrust/weight ratio.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934324
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  • 8
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    Equivalence theorem for constrained optimization of the LegendreK-transform of a concave function (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 25-31 
    Details
    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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934320
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  • 9
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    An approach to the solution of the vector optimization problem of dynamic systems (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 409-422 
    Details
    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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935346
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  • 10
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    A simple procedure for the rapid optimization of reversed-phase separations with ternary mobile phase mixtures (1982)
    Springer
    Chromatographia 15 (1982), S. 688-696 
    Details
    ISSN: 1612-1112
    Schlagwort(e): Reversed-phase LC ; Ternary mobile-phases ; Optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Summary A simple rapid procedure is described for estimating optimum compositions of ternary mobile phase mixtures for the separation of samples by reversed-phase liquid chromatography (RPLC). Retention data in two iso-eluotropic binary mobile phase mixtures (mixtures with equal retention times) are required to initiate the procedure. The logarithm of the capacity factor is assumed to vary linearly with the composition of isoeluotropic ternary mixtures formed by mixing the two limiting binaries. Using the product of resolution factors of adjacent peaks as the criterion, an optimum ternary composition is then calculated. After a chromatogram has been obtained with the predicted optimum ternary mobile phase, the procedure is repeated until no further improvement can be achieved. Examples of the application of the present procedure are described to illustrate its effectiveness.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02261886
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  • 11
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    Fast analysis by gas chromatography (1982)
    Springer
    Chromatographia 15 (1982), S. 125-132 
    Details
    ISSN: 1612-1112
    Schlagwort(e): Capillary columns ; Fast analysis ; Gas chromatography ; Instrumental effects ; Optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Summary The efficiency of fast GC columns depends largely on the quality of the chromatograph. A theoretical and experimental study shows the relative importance of the various phenomena involved and permits the optimization of a GC System. Extremely good performances, exceeding 2,500 plates per second have been routinely obtained.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02290445
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  • 12
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    A chromatographic response function for automated optimization of separations (1982)
    Springer
    Chromatographia 15 (1982), S. 498-504 
    Details
    ISSN: 1612-1112
    Schlagwort(e): Analytical performance ; Chromatographic response function ; HPLC (or LC) ; Optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Summary A chromatographic response function is studied that is sensitive to important criteria of analytical performance: selectivity, accuracy, precision and time required to perform the separation. This function can be applied to mixtures of unknown solutes and little computational effort is needed to evaluate the numerical value of the function from the chromatogram. It shows well defined optima at elution strengths that give minimal elution times simultaneously with good separations in high-performance liquid chromatography. No prior chromatographic information characterizing the expected performance of a system is required. It is possible to use this function without a mechanistic model describing the separation process.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02260283
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  • 13
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    An improved optimization procedure for the selection of mixed mobile phases in reversed phase liquid chromatography (1982)
    Springer
    Chromatographia 16 (1982), S. 48-52 
    Details
    ISSN: 1612-1112
    Schlagwort(e): RP-HPLC ; Optimization ; Complex mobile phases ; Iso-eluotropic mixtures
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Chemie und Pharmazie
    Notizen: Summary The stepwise procedure described previously [1] for the selection of optimal mobile phase compositions in reversed phase liquid chromatography (RPLC) is improved in two ways. The optimization criterion is modified to account for variations in analysis time. The iterative approach to the optimal solvent composition makes a more efficient use of previous data. An example illustrates the resulting gain in speed and accuracy.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02258868
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  • 14
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    Some mathematical aspects of the political business cycle (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 251-275 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Economics ; political cycles ; discrete dynamic systems ; dynamic programming ; optimal control ; Poincaré mapping ; Stieltjes matrix ; optimization in Hilbert space ; infinite horizon ; turnpike theorem
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Under the hypothesis of a myopic electorate, vote-loss-minimizing behavior by the party in power, subject to a dynamic inflation-unemployment relation, is shown to generate an attractive, stable electoral policy cycle. The model presented is derived, with some improvements, from the analogous models of MacRae and Nordhaus. Furthermore, an attempt is made to specify the mathematical aspects of the problem by the Poincaré mapping.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934770
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  • 15
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    On the convergence, invariance, and related aspects of a modification of Huang's algorithm (1982)
    Springer
    Journal of optimization theory and applications 37 (1982), S. 315-341 
    Details
    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.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00935273
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  • 16
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    Numerical solution of minimax problems of optimal control, part 2 (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 111-135 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Minimax problems ; minimax function ; minimax function depending on the state ; minimax function depending on the control ; optimal control ; minimax optimal control ; numerical methods ; computing methods ; transformation techniques ; gradient-restoration algorithms ; sequential gradient-restoration algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In a previous paper (Part 1), we presented general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We considered two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P). In this paper, the transformation techniques presented in Part 1 are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer. Both the single-subarc approach and the multiple-subarc approach are employed. Three test problems characterized by known analytical solutions are solved numerically. It is found that the combination of transformation techniques and sequential gradient-restoration algorithm yields numerical solutions which are quite close to the analytical solutions from the point of view of the minimax performance index. The relative differences between the numerical values and the analytical values of the minimax performance index are of order 10−3 if the single-subarc approach is employed. These relative differences are of order 10−4 or better if the multiple-subarc approach is employed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934326
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  • 17
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    Numerical solution of minimax problems of optimal control, part 1 (1982)
    Springer
    Journal of optimization theory and applications 38 (1982), S. 97-109 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Minimax problems ; minimax function ; minimax function depending on the state ; minimax function depending on the control ; optimal control ; minimax optimal control ; numerical methods ; computing methods ; transformation techniques ; gradient-restoration algorithms ; sequential gradient-restoration algorithms
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract This paper contains general transformation techniques useful to convert minimax problems of optimal control into the Mayer-Bolza problem of the calculus of variations [Problem (P)]. We consider two types of minimax problems: minimax problems of Type (Q), in which the minimax function depends on the state and does not depend on the control; and minimax problems of Type (R), in which the minimax function depends on both the state and the control. Both Problem (Q) and Problem (R) can be reduced to Problem (P). For Problem (Q), we exploit the analogy with a bounded-state problem in combination with a transformation of the Jacobson type. This requires the proper augmentation of the state vectorx(t), the control vectoru(t), and the parameter vector π, as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized. For Problem (R), we exploit the analogy with a bounded-control problem in combination with a transformation of the Valentine type. This requires the proper augmentation of the control vectoru(t) and the parameter vector π, as well as the proper augmentation of the constraining relations. As a result of the transformation, the unknown minimax value of the performance index becomes a component of the parameter vector being optimized. In a subsequent paper (Part 2), the transformation techniques presented here are employed in conjunction with the sequential gradient-restoration algorithm for solving optimal control problems on a digital computer; both the single-subarc approach and the multiple-subarc approach are discussed.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934325
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  • 18
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    Optimal control of a dynamical system representing a gantry crane (1982)
    Springer
    Journal of optimization theory and applications 36 (1982), S. 409-417 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Optimal design ; optimal control ; dynamic systems ; gantry cranes
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Problems arising in the optimal control of gantry crane instaliations are considered. Continuous controls to minimize a control squared objective function are obtained. The amplitude of in-plane oscillations of the suspended mass is assumed small. The optimal controls are sufficiently simple for practical realization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00934354
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  • 19
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    Global optimality of extremals: An example (1982)
    Springer
    Journal of optimization theory and applications 36 (1982), S. 521-534 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Darboux points ; global optimality ; conjugate points ; optimal control
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract The question of the existence and the location of Darboux points (beyond which global optimality is lost) is crucial for minimal sufficient conditions for global optimality and for computation of optimal trajectories. Here, we investigate numerically the Darboux points and their relationship with conjugate points for a problem of minimum fuel, constant velocity, horizontal aircraft turns to capture a line. This simple second-order optimal control problem shows that ignoring the possible existence of Darboux points may play havoc with the computation of optimal trajectories.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF00940545
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