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Special Issue 'International Seminar on Optimization and Related Areas'

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OPTIMIZATION 2017年第8期66卷 1235-1236页

作者： Martinez-Legaz, Juan Enrique Ocana Anaya, Eladio Ruckmann, Jan-Joachim

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Evolutionary Global Optimization, Manifolds and Applications 1st ed. 2016

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丛书名： Studies in Systems, Decision and Control

2016年

作者： Hime Aguiar e Oliveira Junior

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The Aizenberg formula in nonconvex domains and some of its applications

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Journal of Mathematical Sciences 2012年第5期182卷 699-713页

作者： Rotkevich, A. St. Petersburg State University St. Petersburg Russian Federation

The paper concerns the operator determined by the kernel of the Aizenberg integral representation for holomorphic functions. A special class of domains such that this operator acts from C _∞ (∂Ω) to H _∞ (Ω) is introduced. An example of a nonconvex domain that belongs to this class described. Bibliography: 4 titles. © 2012 Springer Science+Business Media, Inc.

关键词： MATHEMATICAL formulas nonconvex programming OPERATOR theory KERNEL functions INTEGRAL representations HOLOMORPHIC functions

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A decomposition approach for global optimum search in QP, NLP and MINLP problems

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Annals of Operations Research 1990年第1期25卷 119-145页

作者： Aggarwal, Avanish Floudas, Christodoulos A. Department of Chemical Engineering Princeton University Princeton 08544-5263 NJ United States

nonconvex programming problems are frequently encountered in engineering and operations research. A large variety of global optimization algorithms have been proposed for the various classes of programming problems. A new approach for global optimum search is presented in this paper which involves a decomposition of the variable set into two sets -complicating and noncomplicating variables. This results in a decomposition of the constraint set leading to two subproblems. The decomposition of the original problem induces special structure in the resulting subproblems and a series of these subproblems are then solved, using the Generalized Benders' Decomposition technique, to determine the optimal solution. The key idea is to combine a judicious selection of the complicating variables with suitable transformations leading to subproblems which can attain their respective global solutions at each iteration. Mathematical properties of the proposed approach are presented. Even though the proposed approach cannot guarantee the determination of the global optimum, computational experience on a number of nonconvex QP, NLP and MINLP example problems indicates that a global optimum solution can be obtained from various starting points. © 1990 J.C. Baltzer A.G. Scientific Publishing Company.

关键词： MATHEMATICAL programming ENGINEERING OPERATIONS research ALGORITHMS nonconvex programming

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Towards an example of a nonconvex monotone follower control problem

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Journal of Mathematical Sciences 2009年第2期161卷 235-249页

作者： Luttamaguzi, J. Department of Mathematics and Computer Science Elizabeth City State University Elizabeth City NC 27909 United States

A one-dimensional monotone follower control problem with a nonconvex Lagrangian is considered. The control problem consists in tracking a standard Wiener process by an adapted nondecreasing process starting at 0. The verification theorem for the problem is presented. The optimal control and the value function are explicitly defined. For some values of parameters of the problem, it is shown that the value function belongs to C². An interesting feature of the optimally controlled state process is that for some initial states it has jumps at times other than the inital time. © 2009 Springer Science+Business Media, Inc.

关键词： LAGRANGIAN functions BROWNIAN motion processes MONOTONE operators VERIFICATION of numerical calculations nonconvex programming

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On the two-dimensional rotational body of maximal Newtonian resistance

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Journal of Mathematical Sciences 2009年第6期161卷 811-819页

作者： Gouveia, P.D.F. Plakhov, A.Yu. Torres, D.F.M. Bragança Polytechnic Institute Bragança Portugal University of Wales Aberystwyth Ceredigion United Kingdom Universidade de Aveiro Aveiro Portugal

We investigate, by means of computer simulations, shapes of nonconvex bodies that maximize resistance to their motion through a rarefied medium, considering that the bodies are moving forward and at the same time slowly rotating. A two-dimensional geometric shape that confers to the body a resistance very close to the theoretical supremum value is obtained, which improves previous results. © 2009 Springer Science+Business Media, Inc.

关键词： NEWTON'S law of gravitation nonconvex programming COMPUTER simulation GEOMETRIC analysis MATHEMATICAL optimization

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Solving nonlinear bilevel programming models of the equilibrium network design problem: A comparative review

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Annals of Operations Research 1992年第1期34卷 203-218页

作者： Suh, Sunduck Kim, Tschangho John Korea Transport Research Institute Seoul South Korea Departments of Urban and Regional Planning and of Civil Engineering University of Illinois at Urbana-Champaign Urbana 61801 IL United States

Nonlinear bilevel programming problems, of which the equilibrium network design problem is one, are extremely difficult to solve. Even if an optimum solution is obtained, there is no sure way of knowing whether the solution is the global optimum or not, due to the nonconvexity of the bilevel programming problem. This paper reviews and discusses recent developments in solution methodologies for nonlinear programming models of the equilibrium network design problem. In particular, it provides a primer for descent-type algorithms reported in the technical literature and proposes certain enhancements thereof. © 1992 J.C. Baltzer AG, Scientific Publishing Company.

关键词： NONLINEAR programming MATHEMATICAL programming COMPUTER networks MATHEMATICAL analysis OPERATIONS research EQUILIBRIUM nonconvex programming TECHNICAL literature

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Une méthode d'optimisation stochastique pour évaluer des minima à ε près

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Bulletin des Sciences Mathematiques 2002年第8期126卷 693-703页

作者： Le Brizaut, Jean-Sébastien Laboratoire Jean Leray (UMR CNRS 6629) Ecole Centrale De Nantes 44321 Nantes cedex 03 BP 92101 France

Minima of nonconvex functionals acting on the Euclidean space are determined by stochastic methods. Feasible conditions for the algotihms are stated. © 2002 Éditions scientifiques et médicales Elsevier ... 详细信息

关键词： MAXIMA & minima nonconvex programming STOCHASTIC processes ALGORITHMS

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Global optimization for molecular conformation problems

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Annals of Operations Research 1993年第1期42卷 85-117页

作者： Maranas, Costas D. Floudas, Christodoulos A. Department of Chemical Engineering Princeton University Princeton 08544-5263 NJ United States

A primal-relaxed dual global optimization algorithm is presented along with an extensive review for finding the global minimum energy configurations of microclusters composed by particles interacting with any type of two-body central forces. First, the original nonconvex expression for the total potential energy is transformed to the difference of two convex functions (DC transformation) via an eigenvalue analysis performed for each pair potential that constitutes the total potential energy function. Then, a decomposition strategy based on the GOP algorithm [1-4] is designed to provide tight upper and lower bounds on the global minimum through the solutions of a sequence of relaxed dual subproblems. A number of theoretical results are included which expedite the computational effort by exploiting the special mathematical structure of the problem. The proposed approach attains ε-convergence to the global minimum in a finite number of iterations. Based on this procedure global optimum solutions are generated for small Lennard-Jones and Morse (a=3) microclusters n≤7. For larger clusters (8≤N≤24 for Lennard-Jones and 8≤N≤30 for Morse), tight lower and upper bounds on the global solution are provided which serve as excellent initial points for local optimization approaches. © 1993 J.C. Baltzer AG, Science Publishers.

关键词： MATHEMATICAL optimization ALGORITHMS OPERATIONS research MATHEMATICAL programming MICROCLUSTERS nonconvex programming

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Feature extraction algorithms for constrained global optimization II. Batch process scheduling application

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Annals of Operations Research 1993年第1期42卷 275-312页

作者： Tsirukis, Athanasios G. Reklaitis, Gintaras V. School of Chemical Engineering Purdue University West Lafayette 47907 IN United States

The feature extraction algorithms developed in part I of this series are applied to solve nonconvex mixed integer nonlinear programming problems which arise in the optimal scheduling of multipurpose chemical plants. A general formulation of the multipurpose plant scheduling problem is developed which considers the allocation of plant equipment and secondary, limited resources to recipe operations so as to satisfy given production requirements while minimizing cost. Results obtained with a test example involving 135 binary and 922 continuous variables show that the successive refinement strategy is effective in identifying dominant regions of the solution space. Furthermore it is shown that multiple moment based characterization methods are superior to the interval analysis method reported in the literature. Trials using a second, larger nonlinear test problem involving 356 binary and 2402 continuous variables demonstrate that the focused successive refinement strategy is more efficient than a constant resolution strategy which employs genetic algorithm constructions. Although the conventional genetic algorithm can be significantly improved by introducing a heuristic mutation strategy which increases the likelihood of constant feasibility, the successive refinement strategy remains dominant. These studies demonstrate that the feature extraction strategy employing successive refinements and relatively low order moment based region characterization methods, offers an effective approach to solving an important class of large scale MINLP problems with multiple local optima. © 1993 J.C. Baltzer AG, Science Publishers.

关键词： ALGORITHMS CHEMICAL plants MATHEMATICAL programming nonconvex programming INTERVAL analysis (Mathematics) GENETIC algorithms NUMERICAL analysis COMBINATORIAL optimization

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