Bøger i Nonconvex Optimization and Its Applications serien

The volume, devoted to variational analysis and its applications, collects selected and refereed contributions, which provide an outline of the field. The meeting of the title "e;Equilibrium Problems and Variational Models"e;, which was held in Erice (Sicily) in the period June 23 - July 2 2000, was the occasion of the presentation of some of these papers; other results are a consequence of a fruitful and constructive atmosphere created during the meeting. New results, which enlarge the field of application of variational analysis, are presented in the book; they deal with the vectorial analysis, time dependent variational analysis, exact penalization, high order deriva- tives, geometric aspects, distance functions and log-quadratic proximal methodology. The new theoretical results allow one to improve in a remarkable way the study of significant problems arising from the applied sciences, as continuum model of transportation, unilateral problems, multicriteria spatial price models, network equilibrium problems and many others. As noted in the previous book "e;Equilibrium Problems: Nonsmooth Optimization and Variational Inequality Models"e;, edited by F. Giannessi, A. Maugeri and P.M. Pardalos, Kluwer Academic Publishers, Vol. 58 (2001), the progress obtained by variational analysis has permitted to han- dle problems whose equilibrium conditions are not obtained by the mini- mization of a functional. These problems obey a more realistic equilibrium condition expressed by a generalized orthogonality (complementarity) con- dition, which enriches our knowledge of the equilibrium behaviour. Also this volume presents important examples of this formulation.

In 1995 the Handbook of Global Optimization (first volume), edited by R. Horst, and P.M. Pardalos, was published. This second volume of the Handbook of Global Optimization is comprised of chapters dealing with modern approaches to global optimization, including different types of heuristics.Topics covered in the handbook include various metaheuristics, such as simulated annealing, genetic algorithms, neural networks, taboo search, shake-and-bake methods, and deformation methods. In addition, the book contains chapters on new exact stochastic and deterministic approaches to continuous and mixed-integer global optimization, such as stochastic adaptive search, two-phase methods, branch-and-bound methods with new relaxation and branching strategies, algorithms based on local optimization, and dynamical search. Finally, the book contains chapters on experimental analysis of algorithms and software, test problems, and applications.

There has been much recent progress in global optimization algo­ rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun­ damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon­ vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en­ dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech­ nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut­ ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti­ mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming.

Optimum Design 2000

This book examines geometric branch-and-bound methods, such as in Lipschitzian optimization, d.c. programming and interval analysis, introduces a new concept for the rate of convergence and also analyzes several bounding operations reported in the literature.

Linking singularity and transversality theory with non-smooth optimization, this book examines complementarity-constrained mathematical programs, semi-infinite programming problems, mathematical programs with vanishing constraints, and bi-level optimization.

This book is devoted to the study and optimization of spatiotemporal stochastic processes - processes which develop simultaneously in space and time under random influences. The book presents problems and content not considered in other books on controlled Markov processes, especially regarding controlled Markov fields on graphs.

This book is the first to discuss complementarity theory and variational inequalities using Leray-Schauder type alternatives. Complementarity theory, a relatively new domain in applied mathematics, has deep connections with several aspects of fundamental mathematics.

Focuses on the progress in turnpike theory. This book presents a number of results concerning the turnpike properties in the calculus of variations and optimal control . These results show that the turnpike properties form a general phenomenon which holds for various classes of variational problems and optimal control problems.

Excepting Sections 1 and 3 in Chapter 1 and Sections 1 and 3 in Chapter 2, the material is new in comparison with any other book, representing research topics where the authors contributed.

This book discusses the Kuhn-Tucker Optimality, Karush-Kuhn-Tucker Necessary and Sufficient Optimality Conditions in presence of various types of generalized convexity assumptions. It details the present state of knowledge on research done in this area.

Chapter 2 lists a number of problems from engineering and economics which give rise to semi-infinite models, including (reverse) Chebyshev approximation, minimax problems, ro bust optimization, design centering, defect minimization problems for operator equations, and disjunctive programming.

This book details algorithms for large-scale unconstrained and bound constrained optimization. It shows optimization techniques from a conjugate gradient algorithm perspective as well as methods of shortest residuals, which have been developed by the author.

Sanchez-Palencia [94] and others stress that it is necessary to consider how thin inclusions/cracks exert their influences onto development of these processes, while such inclusions differ in characteristics from main media to a considerable extent (moisture permeability, permeability to heat, bulk density or shear strength may be mentioned).

Bilevel programming problems are hierarchical optimization problems where the constraints of one problem (the so-called upper level problem) are defined in part by a second parametric optimization problem (the lower level problem).

Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity that have been developed in the last several years.

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems.

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time.

Global optimization problems are extraordinarily di verse and they include economic modeling, fixed charges, finance, networks and transportation, databases and chip design, image processing, nuclear and mechanical design, chemical engineering design and control, molecular biology, and environment al engineering.

Quadratic programs and affine variational inequalities represent two fundamental, closely-related classes of problems in the t,heories of mathematical programming and variational inequalities, resp- tively.

Probabilistic and percentile/quantile functions play an important role in several applications, such as finance (Value-at-Risk), nuclear safety, and the environment.

Global optimization is concerned with the computation and characterization of global optima of nonlinear functions.

Experience gained during a ten-year long involvement in modelling, program ming and application in nonlinear optimization helped me to arrive at the conclusion that in the interest of having successful applications and efficient software production, knowing the structure of the problem to be solved is in dispensable.

Motivation Stochastic Linear Programming with recourse represents one of the more widely applicable models for incorporating uncertainty within in which the SLP optimization models.

This book includes a self-contained theory of inequality problems and their applications to unilateral mechanics. It is the first textbook including a comprehensive and systematic study of both elliptic, parabolic and hyperbolic inequality models, dynamical unilateral systems and unilateral eigenvalues problems.