Continuous Optimization: Current Trends and Modern Applications

ISBN-13: 9781441938947 / Angielski / Miękka / 2010 / 450 str.

V. Jeyakumar; Alexander M. Rubinov

Opis

Continuous optimization is the study of problems in which we wish to opti mize (either maximize or minimize) a continuous function (usually of several variables) often subject to a collection of restrictions on these variables. It has its foundation in the development of calculus by Newton and Leibniz in the 17* DEGREES century. Nowadys, continuous optimization problems are widespread in the mathematical modelling of real world systems for a very broad range of applications. Solution methods for large multivariable constrained continuous optimiza tion problems using computers began with the work of Dantzig in the late 1940s on the simplex method for linear programming problems. Recent re search in continuous optimization has produced a variety of theoretical devel opments, solution methods and new areas of applications. It is impossible to give a full account of the current trends and modern applications of contin uous optimization. It is our intention to present a number of topics in order to show the spectrum of current research activities and the development of numerical methods and applications."

Spis treści

Preface.- PART I. SURVEYS.- Linear Semi-infinite Optimization: Recent Advances (M.A. Goberna).- Some Theoretical Aspects of Newton's Method for Constrained Best Interpolation (H.-D. Qi).- Optimization Methods in Direct and Inverse Scattering (A.G. Ramm, S. Gutman).- On Complexity of Stochastic Programming Problems (A. Shapiro, A. Nemirovski).- Nonlinear Optimization in Modeling Environments: Software Implementations for Compilers, Spreadsheets, Modeling Languages, and Integrated Computing Systems (J.D. Pintér).- Supervised Data Classification via Max-min Separability (A.M. Bagirov, J. Ugon).- A Review of Applications of the Cutting Angle Methods (G. Beliakov).- PART II. THEORY AND NUMERICAL METHODS.- A Numerical Method for Concave Programming Problems (A. Chinchuluun, E. Rentsen, P.M. Pardalos).- Convexification and Monotone Optimization (X. Sun, J. Li, D. Li).- Generalized Lagrange Multipliers for Nonconvex Directionally Differentiable Programs (N. Dinh, G.M. Lee, L.A. Tuan).- Slice Convergence of Sums of Conves Functions in Banach Spaces and Saddle Point Convergence (R. Wenczel, A. Eberhard).- Topical Functions and Their Properties in a Class of Ordered Banach Spaces (H. Mohebi).- PART III. APPLICATIONS.- Dynamical Systems Described by Relational Elasticities with Applications (M. Mammadov, A. Rubinov, J. Yearwood).- Impulsive Control of a Sequence of Rumour Processes (C. Pearce, Y. Kaya, S. Belen).- Minimization of the Sum of Minima of Conves Functions and Its Application to Clustering (A. Rubinov, N. Soukhorokova, J. Ugon).- Analysis of a Practical Control Policy for Water Storage in Two Connected Dams (P. Howlett, J. Piantadosi, C. Pearce).

Blurb

The search for the best possible performance is inherent in human nature. Individuals, enterprises and governments all seek optimal—that is, the best—possible solutions of problems that they meet. Evidently, continuous optimization plays an increasingly significant role in everyday management and technical decisions in science, engineering and commerce.

The collection of 16 refereed papers in this book covers a diverse number of topics and provides a good picture of recent research in continuous optimization. The first part of the book presents substantive survey articles in a number of important topic areas of continuous optimization. Most of the papers in the second part present results on the theoretical aspects as well as numerical methods of continuous optimization. The papers in the third part are mainly concerned with applications of continuous optimization.

Hence, the book will be an additional valuable source of information to faculty, students, and researchers who use continuous optimization to model and solve problems.

 

Audience

This book is intended for researchers in mathematical programming, optimization and operations research; engineers in various fields; and graduate students in applied mathematics, engineering and operations research.