State of the Art in Global Optimization

Optimization problems abound in most fields of science, engineering, and tech­ nology. In many of these problems it is necessary to compute the global optimum (or a good approximation) of a multivariable function. The variables that define the function to be optimized can be continuous and/or discrete and, in addition, many times satisfy certain constraints. Global optimization problems belong to the complexity class of NP-hard prob­ lems. Such problems are very difficult to solve. Traditional descent optimization algorithms based on local information are not adequate for solving these problems. In most cases of practical interest the number of local optima increases, on the aver­ age, exponentially with the size of the problem (number of variables). Furthermore, most of the traditional approaches fail to escape from a local optimum in order to continue the search for the global solution. Global optimization has received a lot of attention in the past ten years, due to the success of new algorithms for solving large classes of problems from diverse areas such as engineering design and control, computational chemistry and biology, structural optimization, computer science, operations research, and economics. This book contains refereed invited papers presented at the conference on "State of the Art in Global Optimization: Computational Methods and Applications" held at Princeton University, April 28-30, 1995. The conference presented current re­ search on global optimization and related applications in science and engineering. The papers included in this book cover a wide spectrum of approaches for solving global optimization problems and applications.

Contenu

Preface. Lagrange Duality in Partly Convex Programming; S. Zlobec. Global Optimization Using Hyperbolic Cross Points; E. Novak, K. Ritter. Global Minimization of Separable Concave Functions under Linear Constraints with Totally Unimodular Matrices; R. Horst, N. Van Thoai. On Existence of Robust Minimizers; S. Shi, et al. A Branch and Bound Algorithm for the Quadratic Assignment Problem Using a Lower Bound Based on Linear Programming; K.G. Ramakrishan, et al. Dynamic Matrix Factorization Methods for Using Formulations Derived from Higher Order Lifting Techniques in the Solution of the Quadratic Assignment Problem; B. Ramachandran, J.K. Pekny. Conical Coercivity Conditions and Global Minimization on Cones. An Existence Result; G. Isac. The Use of Ordinary Differential Equations in Quadratic Maximization with Integer Constraints; P. Maponi, et al. Adaptive Control via Non-Convex Optimization; G.H. Staus, et al. A Decomposition-Based Global Optimization Approach for Solving Bilevel Linear and Quadratic Problems; V. Visweswaran, et al. Generalized TRUST Algorithms for Global Optimization; J. Barhen, V. Protopopescu. Test Results for an Interval Branch and Bound Algorithm for Equality-Constrained Optimization; R.B. Kearfott. Equivalent Methods for Global Optimization; D. MacLagan et al. A C++ Class Library for Interval Arithmetic in Global Optimization; K. Holmqvist, A. Migdalas. On the Convergence of Localisation Search; D.W. Bulger, G.R. Wood. Stochastic Approximation with Smoothing for Optimization of an Adaptive Recursive Filter; W. Edmonson, et al. The Grouping Genetic Algorithm; E. Falkenauer. Accelerating Convergence of Branch-and-Bound Algorithms for Quadratically Constrained Optimization Problems; T. Van Voorhis, F. Al-Khayyal. Distributed Decomposition-based Approaches in Global Optimization; I.P. Androulakis, et al. A Finite Algorithm for Global Minimization of Separable Concave Programs; J.P. Shectman, N.V. Sahinidis. A Pseudo &egr;-Approximate Algorithm for Feedback Vertex Set; T. Qian, et al. Iterative Topographical Global Optimization;A. Torn, S. Viitanen. Global Optimization for the Chemical and Phase Equilibrium Problem Using Interval Analysis; K.I.M. McKinnon, et al. Nonconvex Global Optimization of the Separable Resource Allocation Problem with Continuous Variables; E. Haddad. A d.c. Approach to the Largest Empty Sphere Problem in Higher Dimension; J. Shi, Y. Yoshitsugu. A General D.C. Approach to Location Problems; H. Tuy. Global Optimization by Parallel Constrained Biased Random Search; I. Garcia, G.T. Herman. Global Optimization Problem in Computer Vision; P. Sussner, et al. An Application of Optimization to the Problem of Climate Change; J.A. Filar, et al. Dynamic Visualization in Modelling and Optimization of Ill Defined Problems; W.F. Eddy, A. Mockus. A New Global Optimization Algorithm for Batch Process Scheduling; L. Mockus, G.V. Reklaitis. Nonconvexity and Decent in Nonlinear Programming; A. Lucia, J. Xu. Global Optimization of Chemical Processes Using Stochastic Algorithms; J.R. Banga, W.D. Seider. Logic-Based Outer- Approximation and Benders Decomposition Algorithms for the Synthesis of Process Networks; M. Turkay, I.E. Grossmann. Combinatorially Accelerated Branch-and-Bound Method for Solving the MIP Model of Process Network Synthesis; F. Friedler, et al. Discrete Optimization Using String Encodings for the Synthesis of Complete Chemical Processes; E.S. Fraga.