Optimization

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.

This volume contains many of the papers presented at the conference "e;Optimum Design 2000: Prospects for the New Millennium"e; held in Cardiff, UK on April 12th - 14th, 2000.

In this book, the author considers separable programming and, in particular, one of its important cases - convex separable programming.

Optimum envelope-constrained filter design is concerned with time-domain synthesis of a filter such that its response to a specific input signal stays within prescribed upper and lower bounds, while minimizing the impact of input noise on the filter output or the impact of the shaped signal on other systems depending on the application.

Semi-infinite programming (SIP) deals with optimization problems in which either the number of decision variables or the number of constraints is finite.

As the telecommunication industry introduces new sophisticated technologies, the nature of services and the volume of demands have changed.

This edited book is dedicated to Professor N.

Nonlinear Control Systems and Power System Dynamics presents a comprehensive description of nonlinear control of electric power systems using nonlinear control theory, which is developed by the differential geometric approach and nonlinear robust control method.

Basics of Software Engineering Experimentation is a practical guide to experimentation in a field which has long been underpinned by suppositions, assumptions, speculations and beliefs.

Research in robust control theory has been one of the most active areas of mainstream systems theory since the late 70s.

This volume presents state-of-the-art complementarity applications, algorithms, extensions and theory in the form of eighteen papers.

Decomposition methods aim to reduce large-scale problems to simpler problems.

This volume contains the edited texts of the lectures presented at the Workshop on Nonlinear Optimization held in Erice, Sicily, at the "e;G.

Industrial Mathematics is a relatively recent discipline.

Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches covers recent developments in optimization techniques for addressing several computational chemistry and biology problems.

For a long time the techniques of solving linear optimization (LP) problems improved only marginally.

This volume consists of papers presented in the special sessions on "e;Wave Phenomena and Related Topics"e;, and "e;Asymptotics and Homogenization"e; of the ISAAC'97 Congress held at the University of Delaware, during June 2-7, 1997.

Special tools are required for examining and solving optimization problems.

The Volume on Advances in Steiner Trees is divided into two sections.

People are facing more and more NP-complete or NP-hard problems of a combinatorial nature and of a continuous nature in economic, military and management practice.

Motivated by practical problems in engineering and physics, drawing on a wide range of applied mathematical disciplines, this book is the first to provide, within a unified framework, a self-contained comprehensive mathematical theory of duality for general non-convex, non-smooth systems, with emphasis on methods and applications in engineering mechanics.

Nonlinear Assignment Problems (NAPs) are natural extensions of the classic Linear Assignment Problem, and despite the efforts of many researchers over the past three decades, they still remain some of the hardest combinatorial optimization problems to solve exactly.

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

There has been much recent progress in approximation algorithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective.

Complementarity theory is a new domain in applied mathematics and is concerned with the study of complementarity problems.

2 Radiant sets 236 3 Co-radiant sets 239 4 Radiative and co-radiative sets 241 5 Radiant sets with Lipschitz continuous Minkowski gauges 245 6 Star-shaped sets and their kernels 249 7 Separation 251 8 Abstract convex star-shaped sets 255 References 260 11 DIFFERENCES OF CONVEX COMPACTA AND METRIC SPACES OF CON- 263 VEX COMPACTA WITH APPLICATIONS: A SURVEY A.

The second edition has greatly benefited from a sizable number of comments and suggestions I received from users of the book.

There has been a great deal of excitement in the last ten years over the emer- gence of new mathematical techniques for the analysis and control of nonlinear systems: Witness the emergence of a set of simplified tools for the analysis of bifurcations, chaos, and other complicated dynamical behavior and the develop- ment of a comprehensive theory of geometric nonlinear control.

Significant research activities have taken place in the areas of local and global optimization in the last two decades.

Since I started working in the area of nonlinear programming and, later on, variational inequality problems, I have frequently been surprised to find that many algorithms, however scattered in numerous journals, monographs and books, and described rather differently, are closely related to each other.

Mathematics is playing an ever more important role in the physical and biological sciences, provoking a blurring of boundaries between scientific disciplines and a resurgence of interest in the modem as well as the classical techniques of applied mathematics.

Though the volume covers 22 papers by 36 authors from 12 countries, the history in the background is bound to Hungary where, in 1973 Andras Pnkopa started to lay the foundation of a scientific forum, which can be a regular meeting spot for experts of the world in the field.

Industries rely more and more on advanced technology.

Semi-infinite programming (briefly: SIP) is an exciting part of mathematical programming.

In the early fifties, applied mathematicians, engineers and economists started to pay c10se attention to the optimization problems in which another (lower-Ievel) optimization problem arises as a side constraint.

Due to the general complementary convex structure underlying most nonconvex optimization problems encountered in applications, convex analysis plays an essential role in the development of global optimization methods.

Computer Science and Operations Research continue to have a synergistic relationship and this book - as a part of the Operations Research and Computer Science Interface Series - sits squarely in the center of the confluence of these two technical research communities.

Targeted audience * Specialists in numerical computations, especially in numerical optimiza- tion, who are interested in designing algorithms with automatie result ver- ification, and who would therefore be interested in knowing how general their algorithms caIi in principle be.

The quadratic assignment problem (QAP) was introduced in 1957 by Koopmans and Beckmann to model a plant location problem.

Bayesian decision theory is known to provide an effective framework for the practical solution of discrete and nonconvex optimization problems.

This book deals with decision making in environments of significant data un- certainty, with particular emphasis on operations and production management applications.

In recent years global optimization has found applications in many interesting areas of science and technology including molecular biology, chemical equilibrium problems, medical imaging and networks.

As its title implies, Advances in Multicriteria Analysis presents the most recent developments in multicriteria analysis and in some of its principal areas of application, including marketing, research and development evaluation, financial planning, and medicine.

This book has recently been  retypeset in LaTeX for clearer presentation.

In science, engineering and economics, decision problems are frequently modelled by optimizing the value of a (primary) objective function under stated feasibility constraints.

This work grew out of several years of research, graduate seminars and talks on the subject.

This book should be accessible to students who have had a first course in matrix theory.