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Global optimization is concerned with finding the global extremum (maximum or minimum) of a mathematically defined function (the objective function) in some region of interest. In many practical problems it is not known whether the objective function is unimodal in this region; in many cases it has proved to be multimodal. Unsophisticated use of local optimization techniques is normally inefficient for solving such problems. Therefore, more sophisticated methods designed for global optimization, i.e. global optimization methods, are important from a practical point of view. Most methods discussed here assume that the extremum is attained in the interior of the region of interest, i.e., that the problem is essentially unconstrained. Some methods address the general constrained problem. What is excluded is the treatment of methods designed for problems with a special structure, such as quadratic programming with negatively quadratic forms. This book is the first broad treatment of global optimization with an extensive bibliography covering research done both in east and west. Different ideas and methods proposed for global optimization are classified, described and discussed. The efficiency of algorithms is compared by using both artificial test problems and some practical problems. The solutions of two practical design problems are demonstrated and several other applications are referenced. The book aims at aiding in the education, at stimulating the research in the field, and at advising practitioners in using global optimization methods for solving practical problems.

Numerical analysis --- Mathematical optimization --- Stochastic processes --- 681.3*G3 --- 681.3*I53 --- 519.6 --- 681.3*G16 --- 681.3*G4 --- Random processes --- Probabilities --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing) --- Clustering: algorithms; similarity measures (Pattern recognition) --- Computational mathematics. Numerical analysis. Computer programming --- Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 681.3*G4 Mathematical software: algorithm analysis; certification and testing; efficiency; portability; reliability and robustness; verification --- 681.3*G16 Optimization: constrained optimization; gradient methods; integer programming; least squares methods; linear programming; nonlinear programming (Numericalanalysis) --- 519.6 Computational mathematics. Numerical analysis. Computer programming --- 681.3*I53 Clustering: algorithms; similarity measures (Pattern recognition) --- 681.3*G3 Probability and statistics: probabilistic algorithms (including Monte Carlo);random number generation; statistical computing; statistical software (Mathematics of computing) --- Numerical analysis. --- Distribution (Probability theory. --- Statistics. --- Algorithms. --- Engineering. --- Numerical Analysis. --- Probability Theory and Stochastic Processes. --- Statistics, general. --- Complexity. --- Construction --- Industrial arts --- Technology --- Algorism --- Algebra --- Arithmetic --- Statistical analysis --- Statistical data --- Statistical methods --- Statistical science --- Mathematics --- Econometrics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Foundations

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The research of Antanas Zilinskas has focused on developing models for global optimization, implementing and investigating the corresponding algorithms, and applying those algorithms to practical problems. This volume, dedicated to Professor Zilinskas on the occasion of his 60th birthday, contains new survey papers in which leading researchers from the field present various models and algorithms for solving global optimization problems. Audience This book is intended for scientists and graduate students in computer science and applied mathematics who are interested in optimization algorithms and numerical analysis.

Operational research. Game theory --- Computer. Automation --- automatisering --- informatica --- speltheorie --- wiskunde --- operationeel onderzoek

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Mathematics