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  • Artikel  (12)
  • Global optimization  (12)
  • Springer  (12)
  • American Geophysical Union (AGU)
  • Annual Reviews
  • 1995-1999  (12)
  • 1980-1984
  • 1935-1939
  • 1995  (12)
  • Mathematik  (12)
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  • Artikel  (12)
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  • Springer  (12)
  • American Geophysical Union (AGU)
  • Annual Reviews
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  • 1995-1999  (12)
  • 1980-1984
  • 1935-1939
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  • 1
    Digitale Medien
    Digitale Medien
    An adaptive stochastic global optimization algorithm for one-dimensional functions (1995)
    Springer
    Annals of operations research 58 (1995), S. 261-278 
    Details
    ISSN: 1572-9338
    Schlagwort(e): Global optimization ; Wiener process ; sequential stopping rules ; one-step look-ahead
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik , Wirtschaftswissenschaften
    Notizen: Abstract In this paper a new algorithm is proposed, based upon the idea of modeling the objective function of a global optimization problem as a sample path from a Wiener process. Unlike previous work in this field, in the proposed model the parameter of the Wiener process is considered as a random variable whose conditional (posterior) distribution function is updated on-line. Stopping criteria for Bayesian algorithms are discussed and detailed proofs on finite-time stopping are provided.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02096402
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  • 2
    Digitale Medien
    Digitale Medien
    Pure adaptive search for finite global optimization (1995)
    Springer
    Mathematical programming 69 (1995), S. 443-448 
    Details
    ISSN: 1436-4646
    Schlagwort(e): Global optimization ; Discrete optimization ; Algorithm complexity ; Random search ; Markov chains
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Informatik , Mathematik
    Notizen: Abstract Pure Adaptive Search is a stochastic algorithm which has been analyzed for continuous global optimization. When a uniform distribution is used in PAS, it has been shown to have complexity which is linear in dimension. We define strong and weak variations of PAS in the setting of finite global optimization and prove analogous results. In particular, for then-dimensional lattice {1,⋯,k} n , the expected number of iterations to find the global optimum is linear inn. Many discrete combinatorial optimization problems, although having intractably large domains, have quite small ranges. The strong version of PAS for all problems, and the weak version of PAS for a limited class of problems, has complexity the order of the size of the range.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01585570
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  • 3
    Digitale Medien
    Digitale Medien
    Deletion-by-infeasibility rule for DC-constrained global optimization (1995)
    Springer
    Journal of optimization theory and applications 84 (1995), S. 443-455 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Global optimization ; nonconvex programming ; mathematical programming ; DC-programming ; branch-and-bound methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In Ref. 1, a general class of branch-and-bound methods was proposed by Horst for solving global optimization problems. One of the main contributions of Ref. 1 was the opportunity of handling partition elements whose feasibility is not known. Deletion-by-infeasibility rules were presented for problems where the feasible set is convex, is defined by finitely many convex and reverse convex constraints, or is defined by Lipschitzian inequalities. In this note, we propose a new deletion-by-infeasibility rule for problems whose feasible set is defined by functions representable as differences of convex functions.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02192125
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  • 4
    Digitale Medien
    Digitale Medien
    An adaptive simulated annealing algorithm for global optimization over continuous variables (1995)
    Springer
    Journal of global optimization 6 (1995), S. 1-37 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Global optimization ; simulated annealing ; Monte Carlo optimization
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A method is presented for attempting global minimization for a function of continuous variables subject to constraints. The method, calledAdaptive Simulated Annealing (ASA), is distinguished by the fact that the fixed temperature schedules and step generation routines that characterize other implementations are here replaced by heuristic-based methods that effectively eliminate the dependence of the algorithm's overall performance on user-specified control parameters. A parallelprocessing version of ASA that gives increased efficiency is presented and applied to two standard problems for illustration and comparison.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01106604
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  • 5
    Digitale Medien
    Digitale Medien
    New LP bound in multivariate Lipschitz optimization: Theory and applications (1995)
    Springer
    Journal of optimization theory and applications 86 (1995), S. 369-388 
    Details
    ISSN: 1573-2878
    Schlagwort(e): Global optimization ; Lipschitz optimization ; systems of inequalities ; branch-and-bounds methods
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Most numerically promising methods for solving multivariate unconstrained Lipschitz optimization problems of dimension greater than two use rectangular or simplicial branch-and-bound techniques with computationally cheap but rather crude lower bounds. Generalizations to constrained problems, however, require additional devices to detect sufficiently many infeasible partition sets. In this article, a new lower bounding procedure is proposed for simplicial methods yielding considerably better bounds at the expense of two linear programs in each iteration. Moreover, the resulting approach can solve easily linearly constrained problems, since in this case infeasible partition sets are automatically detected by the lower bounding procedure. Finally, it is shown that the lower bounds can be further improved when the method is applied to solve systems of inequalities. Implementation issues, numerical experiments, and comparisons are discussed in some detail.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF02192085
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  • 6
    Digitale Medien
    Digitale Medien
    Global optimization of arborescent multilevel inventory systems (1995)
    Springer
    Journal of global optimization 6 (1995), S. 269-292 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Global optimization ; inventory problems ; discrete Hamilton-Jacobi-Bellman equations ; quasi-variational inequalities ; subsolutions and supersolutions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract We consider the numerical resolution of hierarchical inventory problems under global optimization. First we describe the model as well as the dynamical stochastic system and the impulse controls involved. Next we characterize the optimal cost function and we formulate the Hamilton-Jacobi-Bellman equations. We present a numerical scheme and a fast algorithm of resolution, with a result on the speed of convergence. Finally, we apply the discretization method to some examples where we show the usefulness of the proposed numerical method as well as the advantages of operating under global optimization.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01099465
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  • 7
    Digitale Medien
    Digitale Medien
    A branch and bound algorithm for bound constrained optimization problems without derivatives (1995)
    Springer
    Journal of global optimization 7 (1995), S. 297-331 
    Details
    ISSN: 1573-2916
    Schlagwort(e): 49D37 ; 65G10 ; Global optimization ; interval arithmetic
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper, we give a new branch and bound algorithm for the global optimization problem with bound constraints. The algorithm is based on the use of inclusion functions. The bounds calculated for the global minimum value are proved to be correct, all rounding errors are rigorously estimated. Our scheme attempts to exclude most “uninteresting” parts of the search domain and concentrates on its “promising” subsets. This is done as fast as possible (by involving local descent methods), and uses little information as possible (no derivatives are required). Numerical results for many well-known problems as well as some comparisons with other methods are given.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01279453
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  • 8
    Digitale Medien
    Digitale Medien
    Simple global minimization algorithm for one-variable rational functions (1995)
    Springer
    Journal of global optimization 6 (1995), S. 293-311 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Global optimization ; univariate optimization ; polynomials ; rational functions ; Storm's chain
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract Sturm's chain technique for evaluation of a number of real roots of polynomials is applied to construct a simple algorithm for global optimization of polynomials or generally for rational functions of finite global minimal value. The method can be applied both to find the global minimum in an interval or without any constraints. It is shown how to use the method to minimize globally a truncated Fourier series. The results of numerical tests are presented and discussed. The cost of the method scales as the square of the degree of the polynomial.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01099466
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  • 9
    Digitale Medien
    Digitale Medien
    On the selection of subdivision directions in interval branch-and-bound methods for global optimization (1995)
    Springer
    Journal of global optimization 7 (1995), S. 183-207 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Global optimization ; interval arithmetic ; branch-and-bound ; interval subdivision
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract This paper investigates the influence of the interval subdivision selection rule on the convergence of interval branch-and-bound algorithms for global optimization. For the class of rules that allows convergence, we study the effects of the rules on a model algorithm with special list ordering. Four different rules are investigated in theory and in practice. A wide spectrum of test problems is used for numerical tests indicating that there are substantial differences between the rules with respect to the required CPU time, the number of function and derivative evaluations, and the necessary storage space. Two rules can provide considerable improvements in efficiency for our model algorithm.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01097060
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  • 10
    Digitale Medien
    Digitale Medien
    An algorithm for solving global optimization problems with nonlinear constraints (1995)
    Springer
    Journal of global optimization 7 (1995), S. 407-419 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Global optimization ; nonlinear constraints ; local tuning ; index scheme ; global convergence
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract In this paper we propose an algorithm using only the values of the objective function and constraints for solving one-dimensional global optimization problems where both the objective function and constraints are Lipschitzean and nonlinear. The constrained problem is reduced to an unconstrained one by the index scheme. To solve the reduced problem a new method with local tuning on the behavior of the objective function and constraints over different sectors of the search region is proposed. Sufficient conditions of global convergence are established. We also present results of some numerical experiments.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01099650
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  • 11
    Digitale Medien
    Digitale Medien
    Finding all solutions of nonlinearly constrained systems of equations (1995)
    Springer
    Journal of global optimization 7 (1995), S. 143-182 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Global optimization ; nonlinear systems of equations ; all solutions
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A new approach is proposed for finding allε-feasible solutions for certain classes of nonlinearly constrained systems of equations. By introducing slack variables, the initial problem is transformed into a global optimization problem (P) whose multiple global minimum solutions with a zero objective value (if any) correspond to all solutions of the initial constrained system of equalities. Allε-globally optimal points of (P) are then localized within a set of arbitrarily small disjoint rectangles. This is based on a branch and bound type global optimization algorithm which attains finiteε-convergence to each of the multiple global minima of (P) through the successive refinement of a convex relaxation of the feasible region and the subsequent solution of a series of nonlinear convex optimization problems. Based on the form of the participating functions, a number of techniques for constructing this convex relaxation are proposed. By taking advantage of the properties of products of univariate functions, customized convex lower bounding functions are introduced for a large number of expressions that are or can be transformed into products of univariate functions. Alternative convex relaxation procedures involve either the difference of two convex functions employed in αBB [23] or the exponential variable transformation based underestimators employed for generalized geometric programming problems [24]. The proposed approach is illustrated with several test problems. For some of these problems additional solutions are identified that existing methods failed to locate.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01097059
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  • 12
    Digitale Medien
    Digitale Medien
    αBB: A global optimization method for general constrained nonconvex problems (1995)
    Springer
    Journal of global optimization 7 (1995), S. 337-363 
    Details
    ISSN: 1573-2916
    Schlagwort(e): Global optimization ; constrained optimization ; convex relaxation
    Quelle: Springer Online Journal Archives 1860-2000
    Thema: Mathematik
    Notizen: Abstract A branch and bound global optimization method,αBB, for general continuous optimization problems involving nonconvexities in the objective function and/or constraints is presented. The nonconvexities are categorized as being either of special structure or generic. A convex relaxation of the original nonconvex problem is obtained by (i) replacing all nonconvex terms of special structure (i.e. bilinear, fractional, signomial) with customized tight convex lower bounding functions and (ii) by utilizing the α parameter as defined in [17] to underestimate nonconvex terms of generic structure. The proposed branch and bound type algorithm attains finiteε-convergence to the global minimum through the successive subdivision of the original region and the subsequent solution of a series of nonlinear convex minimization problems. The global optimization method,αBB, is implemented in C and tested on a variety of example problems.
    Materialart: Digitale Medien
    URL: http://dx.doi.org/10.1007/BF01099647
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