This book introduces a novel approach to discrete optimization, providing both theoretical insights and algorithmic developments that lead to improvements over state-of-the-art technology. The authors present chapters on the use of decision diagrams for combinatorial optimization and constraint programming, with attention to general-purpose solution methods as well as problem-specific techniques. The book will be useful for researchers and practitioners in discrete optimization and constraint programming. "Decision Diagrams for Optimization is one of the most exciting developments emerging from constraint programming in recent years. This book is a compelling summary of existing results in this space and a must-read for optimizers around the world." [Pascal Van Hentenryck]
This book presents the main methodological and theoretical developments in stochastic global optimization. The extensive text is divided into four chapters; the topics include the basic principles and methods of global random search, statistical inference in random search, Markovian and population-based random search methods, methods based on statistical models of multimodal functions and principles of rational decisions theory.
Key features: Inspires readers to explore various stochastic methods of global optimization by clearly explaining the main methodological principles and features of the methods; Includes a comprehensive study of probabilistic and statistical models underlying the stochastic optimization algorithms; Expands upon more sophisticated techniques including random and semi-random coverings, stratified sampling schemes, Markovian algorithms and population based algorithms; Provides a thorough description of the methods based on statistical models of objective function; Discusses criteria for evaluating efficiency of optimization algorithms and difficulties occurring in applied global optimization.
"Nonsmooth Optimization Methods and Applications" provides an overview of this branch of mathematics, concentrating on the interaction between the theory and its applications. The topics covered include: generalization of convexity, invexity, coercivity, monotonicity and pseudoconvexity; generalization of differentiability of functions and multifunctions, and their applications to extremum problems; variational and hemivariational inequalities and their applications to mechanics and operations research; calculus for non-differentiable functions and new developments in the calculus of variations; stability of mathematical programs; Lagrangian multipliers and augmented Langrangian theory; penalty methods; vector extremum problems and methods for solving non-differentiable extremum problems, in particular bundle methods.
Six Characters in Search of an Author (Italian: Sei personaggi in cerca d'autore) is a 1921 Italian play by Luigi Pirandello, first performed in that same year. An absurdist metatheatrical play about the relationship between authors, their characters, and theatre practitioners, it premiered at the Teatro Valle in Rome to a mixed reception, with shouts from the audience of "Manicomio!" ("Madhouse!"), though the reception improved at subsequent performances - helped when Pirandello provided for the play's third edition, published in 1925, a foreword clarifying its structure and ideas. The play had its American premiere in 1922 on Broadway at the Princess Theatre, and was performed for over a year off-Broadway at the Martinique Theatre beginning in 1963. An acting company prepares to rehearse the play The Rules of the Game by Luigi Pirandello. As the rehearsal is about to begin the play is unexpectedly interrupted by the arrival of six strange people...
Although a useful and important tool, the potential of mathematical modelling for decision making is often neglected. Considered an art by many and weird science by some, modelling is not as widely appreciated in problem solving and decision making as perhaps it should be. And although many operations research, management science, and optimization books touch on modelling techniques, the short shrift they usually get in coverage is reflected in their minimal application to problems in the real world. Illustrating the important influence of modelling on the decision making process, Optimization Modelling: A Practical Approach helps you come to grips with a wide range of modelling techniques.
Highlighting the modelling aspects of optimization problems, the authors present the techniques in a clear and straightforward manner, illustrated by examples. They provide and analyze the formulation and modelling of a number of well-known theoretical and practical problems and touch on solution approaches. The book demonstrates the use of optimization packages through the solution of various mathematical models and provides an interpretation of some of those solutions. It presents the practical aspects and difficulties of problem solving and solution implementation and studies a number of practical problems. The book also discusses the use of available software packages in solving optimization models without going into difficult mathematical details and complex solution methodologies.
The emphasis on modelling techniques rather than solution algorithms sets this book apart. It is a single source for a wide range of methods, classic theoretical and practical problems, data collection and input preparation, the use of different optimization software, and practical issues of modelling, model solving, and implementation. The authors draw directly from their experience to provide lessons learned when applying modelling techniques to practical problem solving and implementation difficulties.
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