Foundations of Mathematical Optimization
Foundations of Mathematical Optimization

Author: Diethard Ernst Pallaschke

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 597

ISBN-13: 9401715882

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Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization. Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.

Foundations of Optimization
Foundations of Optimization

Author: Osman Güler

Publisher: Springer Science & Business Media

Published: 2010-08-03

Total Pages: 445

ISBN-13: 0387684077

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This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.

Mathematical Theory of Optimization
Mathematical Theory of Optimization

Author: Ding-Zhu Du

Publisher: Springer Science & Business Media

Published: 2013-03-14

Total Pages: 277

ISBN-13: 1475757956

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This book provides an introduction to the mathematical theory of optimization. It emphasizes the convergence theory of nonlinear optimization algorithms and applications of nonlinear optimization to combinatorial optimization. Mathematical Theory of Optimization includes recent developments in global convergence, the Powell conjecture, semidefinite programming, and relaxation techniques for designs of approximation solutions of combinatorial optimization problems.

Optimization
Optimization

Author: H. Ronald Miller

Publisher: John Wiley & Sons

Published: 2011-03-29

Total Pages: 676

ISBN-13: 1118031180

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A thorough and highly accessible resource for analysts in a broadrange of social sciences. Optimization: Foundations and Applications presents a series ofapproaches to the challenges faced by analysts who must find thebest way to accomplish particular objectives, usually with theadded complication of constraints on the available choices.Award-winning educator Ronald E. Miller provides detailed coverageof both classical, calculus-based approaches and newer,computer-based iterative methods. Dr. Miller lays a solid foundation for both linear and nonlinearmodels and quickly moves on to discuss applications, includingiterative methods for root-finding and for unconstrainedmaximization, approaches to the inequality constrained linearprogramming problem, and the complexities of inequality constrainedmaximization and minimization in nonlinear problems. Otherimportant features include: More than 200 geometric interpretations of algebraic results,emphasizing the intuitive appeal of mathematics Classic results mixed with modern numerical methods to aidusers of computer programs Extensive appendices containing mathematical details importantfor a thorough understanding of the topic With special emphasis on questions most frequently asked by thoseencountering this material for the first time, Optimization:Foundations and Applications is an extremely useful resource forprofessionals in such areas as mathematics, engineering, economicsand business, regional science, geography, sociology, politicalscience, management and decision sciences, public policy analysis,and numerous other social sciences. An Instructor's Manual presenting detailed solutions to all theproblems in the book is available upon request from the Wileyeditorial department.

Foundations of Optimization
Foundations of Optimization

Author: M. S. Bazaraa

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 203

ISBN-13: 3642482945

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Current1y there is a vast amount of literature on nonlinear programming in finite dimensions. The pub1ications deal with convex analysis and severa1 aspects of optimization. On the conditions of optima1ity they deal mainly with generali- tions of known results to more general problems and also with less restrictive assumptions. There are also more general results dealing with duality. There are yet other important publications dealing with algorithmic deve10pment and their applications. This book is intended for researchers in nonlinear programming, and deals mainly with convex analysis, optimality conditions and duality in nonlinear programming. It consolidates the classic results in this area and some of the recent results. The book has been divided into two parts. The first part gives a very comp- hensive background material. Assuming a background of matrix algebra and a senior level course in Analysis, the first part on convex analysis is self-contained, and develops some important results needed for subsequent chapters. The second part deals with optimality conditions and duality. The results are developed using extensively the properties of cones discussed in the first part. This has faci- tated derivations of optimality conditions for equality and inequality constrained problems. Further, minimum-principle type conditions are derived under less restrictive assumptions. We also discuss constraint qualifications and treat some of the more general duality theory in nonlinear programming.

Practical Mathematical Optimization
Practical Mathematical Optimization

Author: Jan Snyman

Publisher: Springer Science & Business Media

Published: 2005-12-15

Total Pages: 271

ISBN-13: 0387243496

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This book presents basic optimization principles and gradient-based algorithms to a general audience, in a brief and easy-to-read form. It enables professionals to apply optimization theory to engineering, physics, chemistry, or business economics.

Foundations of Mathematical Optimization
Foundations of Mathematical Optimization

Author: Diethard Pallaschke

Publisher: Springer Science & Business Media

Published: 1997-02-28

Total Pages: 608

ISBN-13: 9780792344247

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Many books on optimization consider only finite dimensional spaces. This volume is unique in its emphasis: the first three chapters develop optimization in spaces without linear structure, and the analog of convex analysis is constructed for this case. Many new results have been proved specially for this publication. In the following chapters optimization in infinite topological and normed vector spaces is considered. The novelty consists in using the drop property for weak well-posedness of linear problems in Banach spaces and in a unified approach (by means of the Dolecki approximation) to necessary conditions of optimality. The method of reduction of constraints for sufficient conditions of optimality is presented. The book contains an introduction to non-differentiable and vector optimization. Audience: This volume will be of interest to mathematicians, engineers, and economists working in mathematical optimization.

Foundations of Applied Mathematics, Volume 2
Foundations of Applied Mathematics, Volume 2

Author: Jeffrey Humpherys

Publisher: SIAM

Published: 2020-03-10

Total Pages: 807

ISBN-13: 1611976065

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In this second book of what will be a four-volume series, the authors present, in a mathematically rigorous way, the essential foundations of both the theory and practice of algorithms, approximation, and optimization—essential topics in modern applied and computational mathematics. This material is the introductory framework upon which algorithm analysis, optimization, probability, statistics, machine learning, and control theory are built. This text gives a unified treatment of several topics that do not usually appear together: the theory and analysis of algorithms for mathematicians and data science students; probability and its applications; the theory and applications of approximation, including Fourier series, wavelets, and polynomial approximation; and the theory and practice of optimization, including dynamic optimization. When used in concert with the free supplemental lab materials, Foundations of Applied Mathematics, Volume 2: Algorithms, Approximation, Optimization teaches not only the theory but also the computational practice of modern mathematical methods. Exercises and examples build upon each other in a way that continually reinforces previous ideas, allowing students to retain learned concepts while achieving a greater depth. The mathematically rigorous lab content guides students to technical proficiency and answers the age-old question “When am I going to use this?” This textbook is geared toward advanced undergraduate and beginning graduate students in mathematics, data science, and machine learning.

Mathematical Optimization and Economic Theory
Mathematical Optimization and Economic Theory

Author: Michael D. Intriligator

Publisher: SIAM

Published: 2002-01-01

Total Pages: 515

ISBN-13: 0898715113

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A classic account of mathematical programming and control techniques and their applications to static and dynamic problems in economics.

Variational Methods for Structural Optimization
Variational Methods for Structural Optimization

Author: Andrej Cherkaev

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 561

ISBN-13: 1461211883

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This book bridges a gap between a rigorous mathematical approach to variational problems and the practical use of algorithms of structural optimization in engineering applications. The foundations of structural optimization are presented in sufficiently simple form as to make them available for practical use.