Convex Analysis And Global Optimization

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Convex Analysis and Global Optimization

Author : Hoang Tuy
Publisher : Springer Science & Business Media
ISBN 13 : 1475728093
Total Pages : 346 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Convex Analysis and Global Optimization by : Hoang Tuy

Download or read book Convex Analysis and Global Optimization written by Hoang Tuy and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.

Convex Analysis and Global Optimization

Author : Hoang Tuy
Publisher : Springer Science & Business Media
ISBN 13 : 9780792348184
Total Pages : 362 pages
Book Rating : 4.3/5 (481 download)

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Book Synopsis Convex Analysis and Global Optimization by : Hoang Tuy

Download or read book Convex Analysis and Global Optimization written by Hoang Tuy and published by Springer Science & Business Media. This book was released on 1998-01-31 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. This book develops a coherent and rigorous theory of deterministic global optimization from this point of view. Part I constitutes an introduction to convex analysis, with an emphasis on concepts, properties and results particularly needed for global optimization, including those pertaining to the complementary convex structure. Part II presents the foundation and application of global search principles such as partitioning and cutting, outer and inner approximation, and decomposition to general global optimization problems and to problems with a low-rank nonconvex structure as well as quadratic problems. Much new material is offered, aside from a rigorous mathematical development. Audience: The book is written as a text for graduate students in engineering, mathematics, operations research, computer science and other disciplines dealing with optimization theory. It is also addressed to all scientists in various fields who are interested in mathematical optimization.

Advances in Convex Analysis and Global Optimization

Author : Nicolas Hadjisavvas
Publisher : Springer Science & Business Media
ISBN 13 : 146130279X
Total Pages : 601 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Advances in Convex Analysis and Global Optimization by : Nicolas Hadjisavvas

Download or read book Advances in Convex Analysis and Global Optimization written by Nicolas Hadjisavvas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 601 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has been much recent progress in global optimization algo rithms for nonconvex continuous and discrete problems from both a theoretical and a practical perspective. Convex analysis plays a fun damental role in the analysis and development of global optimization algorithms. This is due essentially to the fact that virtually all noncon vex optimization problems can be described using differences of convex functions and differences of convex sets. A conference on Convex Analysis and Global Optimization was held during June 5 -9, 2000 at Pythagorion, Samos, Greece. The conference was honoring the memory of C. Caratheodory (1873-1950) and was en dorsed by the Mathematical Programming Society (MPS) and by the Society for Industrial and Applied Mathematics (SIAM) Activity Group in Optimization. The conference was sponsored by the European Union (through the EPEAEK program), the Department of Mathematics of the Aegean University and the Center for Applied Optimization of the University of Florida, by the General Secretariat of Research and Tech nology of Greece, by the Ministry of Education of Greece, and several local Greek government agencies and companies. This volume contains a selective collection of refereed papers based on invited and contribut ing talks presented at this conference. The two themes of convexity and global optimization pervade this book. The conference provided a forum for researchers working on different aspects of convexity and global opti mization to present their recent discoveries, and to interact with people working on complementary aspects of mathematical programming.

Convex Analysis and Nonlinear Optimization

Author : Jonathan Borwein
Publisher : Springer Science & Business Media
ISBN 13 : 0387312560
Total Pages : 316 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Convex Analysis and Nonlinear Optimization by : Jonathan Borwein

Download or read book Convex Analysis and Nonlinear Optimization written by Jonathan Borwein and published by Springer Science & Business Media. This book was released on 2010-05-05 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: Optimization is a rich and thriving mathematical discipline, and the underlying theory of current computational optimization techniques grows ever more sophisticated. This book aims to provide a concise, accessible account of convex analysis and its applications and extensions, for a broad audience. Each section concludes with an often extensive set of optional exercises. This new edition adds material on semismooth optimization, as well as several new proofs.

Abstract Convexity and Global Optimization

Author : Alexander M. Rubinov
Publisher : Springer Science & Business Media
ISBN 13 : 9780792363231
Total Pages : 516 pages
Book Rating : 4.3/5 (632 download)

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Book Synopsis Abstract Convexity and Global Optimization by : Alexander M. Rubinov

Download or read book Abstract Convexity and Global Optimization written by Alexander M. Rubinov and published by Springer Science & Business Media. This book was released on 2000-05-31 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of two parts. Firstly, the main notions of abstract convexity and their applications in the study of some classes of functions and sets are presented. Secondly, both theoretical and numerical aspects of global optimization based on abstract convexity are examined. Most of the book does not require knowledge of advanced mathematics. Classical methods of nonconvex mathematical programming, being based on a local approximation, cannot be used to examine and solve many problems of global optimization, and so there is a clear need to develop special global tools for solving these problems. Some of these tools are based on abstract convexity, that is, on the representation of a function of a rather complicated nature as the upper envelope of a set of fairly simple functions. Audience: The book will be of interest to specialists in global optimization, mathematical programming, and convex analysis, as well as engineers using mathematical tools and optimization techniques and specialists in mathematical modelling.

Convex Analysis and Optimization

Author : Dimitri Bertsekas
Publisher : Athena Scientific
ISBN 13 : 1886529450
Total Pages : 560 pages
Book Rating : 4.8/5 (865 download)

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Book Synopsis Convex Analysis and Optimization by : Dimitri Bertsekas

Download or read book Convex Analysis and Optimization written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2003-03-01 with total page 560 pages. Available in PDF, EPUB and Kindle. Book excerpt: A uniquely pedagogical, insightful, and rigorous treatment of the analytical/geometrical foundations of optimization. The book provides a comprehensive development of convexity theory, and its rich applications in optimization, including duality, minimax/saddle point theory, Lagrange multipliers, and Lagrangian relaxation/nondifferentiable optimization. It is an excellent supplement to several of our books: Convex Optimization Theory (Athena Scientific, 2009), Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2016), Network Optimization (Athena Scientific, 1998), and Introduction to Linear Optimization (Athena Scientific, 1997). Aside from a thorough account of convex analysis and optimization, the book aims to restructure the theory of the subject, by introducing several novel unifying lines of analysis, including: 1) A unified development of minimax theory and constrained optimization duality as special cases of duality between two simple geometrical problems. 2) A unified development of conditions for existence of solutions of convex optimization problems, conditions for the minimax equality to hold, and conditions for the absence of a duality gap in constrained optimization. 3) A unification of the major constraint qualifications allowing the use of Lagrange multipliers for nonconvex constrained optimization, using the notion of constraint pseudonormality and an enhanced form of the Fritz John necessary optimality conditions. Among its features the book: a) Develops rigorously and comprehensively the theory of convex sets and functions, in the classical tradition of Fenchel and Rockafellar b) Provides a geometric, highly visual treatment of convex and nonconvex optimization problems, including existence of solutions, optimality conditions, Lagrange multipliers, and duality c) Includes an insightful and comprehensive presentation of minimax theory and zero sum games, and its connection with duality d) Describes dual optimization, the associated computational methods, including the novel incremental subgradient methods, and applications in linear, quadratic, and integer programming e) Contains many examples, illustrations, and exercises with complete solutions (about 200 pages) posted at the publisher's web site http://www.athenasc.com/convexity.html

Global Optimization with Non-Convex Constraints

Author : Roman G. Strongin
Publisher : Springer Science & Business Media
ISBN 13 : 146154677X
Total Pages : 717 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Global Optimization with Non-Convex Constraints by : Roman G. Strongin

Download or read book Global Optimization with Non-Convex Constraints written by Roman G. Strongin and published by Springer Science & Business Media. This book was released on 2013-11-09 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything should be made as simple as possible, but not simpler. (Albert Einstein, Readers Digest, 1977) The modern practice of creating technical systems and technological processes of high effi.ciency besides the employment of new principles, new materials, new physical effects and other new solutions ( which is very traditional and plays the key role in the selection of the general structure of the object to be designed) also includes the choice of the best combination for the set of parameters (geometrical sizes, electrical and strength characteristics, etc.) concretizing this general structure, because the Variation of these parameters ( with the structure or linkage being already set defined) can essentially affect the objective performance indexes. The mathematical tools for choosing these best combinations are exactly what is this book about. With the advent of computers and the computer-aided design the pro bations of the selected variants are usually performed not for the real examples ( this may require some very expensive building of sample op tions and of the special installations to test them ), but by the analysis of the corresponding mathematical models. The sophistication of the mathematical models for the objects to be designed, which is the natu ral consequence of the raising complexity of these objects, greatly com plicates the objective performance analysis. Today, the main (and very often the only) available instrument for such an analysis is computer aided simulation of an object's behavior, based on numerical experiments with its mathematical model.

Abstract Convexity and Global Optimization

Author : Alexander M. Rubinov
Publisher : Springer Science & Business Media
ISBN 13 : 1475732007
Total Pages : 506 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Abstract Convexity and Global Optimization by : Alexander M. Rubinov

Download or read book Abstract Convexity and Global Optimization written by Alexander M. Rubinov and published by Springer Science & Business Media. This book was released on 2013-03-14 with total page 506 pages. Available in PDF, EPUB and Kindle. Book excerpt: Special tools are required for examining and solving optimization problems. The main tools in the study of local optimization are classical calculus and its modern generalizions which form nonsmooth analysis. The gradient and various kinds of generalized derivatives allow us to ac complish a local approximation of a given function in a neighbourhood of a given point. This kind of approximation is very useful in the study of local extrema. However, local approximation alone cannot help to solve many problems of global optimization, so there is a clear need to develop special global tools for solving these problems. The simplest and most well-known area of global and simultaneously local optimization is convex programming. The fundamental tool in the study of convex optimization problems is the subgradient, which actu ally plays both a local and global role. First, a subgradient of a convex function f at a point x carries out a local approximation of f in a neigh bourhood of x. Second, the subgradient permits the construction of an affine function, which does not exceed f over the entire space and coincides with f at x. This affine function h is called a support func tion. Since f(y) ~ h(y) for ally, the second role is global. In contrast to a local approximation, the function h will be called a global affine support.

Convex Optimization

Author : Stephen P. Boyd
Publisher : Cambridge University Press
ISBN 13 : 9780521833783
Total Pages : 744 pages
Book Rating : 4.8/5 (337 download)

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Book Synopsis Convex Optimization by : Stephen P. Boyd

Download or read book Convex Optimization written by Stephen P. Boyd and published by Cambridge University Press. This book was released on 2004-03-08 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.

Nonlinear Analysis and Global Optimization

Author : Themistocles M. Rassias
Publisher : Springer Nature
ISBN 13 : 3030617327
Total Pages : 484 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Nonlinear Analysis and Global Optimization by : Themistocles M. Rassias

Download or read book Nonlinear Analysis and Global Optimization written by Themistocles M. Rassias and published by Springer Nature. This book was released on 2021-02-26 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume discusses aspects of nonlinear analysis in which optimization plays an important role, as well as topics which are applied to the study of optimization problems. Topics include set-valued analysis, mixed concave-convex sub-superlinear Schroedinger equation, Schroedinger equations in nonlinear optics, exponentially convex functions, optimal lot size under the occurrence of imperfect quality items, generalized equilibrium problems, artificial topologies on a relativistic spacetime, equilibrium points in the restricted three-body problem, optimization models for networks of organ transplants, network curvature measures, error analysis through energy minimization and stability problems, Ekeland variational principles in 2-local Branciari metric spaces, frictional dynamic problems, norm estimates for composite operators, operator factorization and solution of second-order nonlinear difference equations, degenerate Kirchhoff-type inclusion problems, and more.

Global Optimization

Author : Leo Liberti
Publisher : Springer Science & Business Media
ISBN 13 : 0387305289
Total Pages : 428 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Global Optimization by : Leo Liberti

Download or read book Global Optimization written by Leo Liberti and published by Springer Science & Business Media. This book was released on 2006-06-22 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most global optimization literature focuses on theory. This book, however, contains descriptions of new implementations of general-purpose or problem-specific global optimization algorithms. It discusses existing software packages from which the entire community can learn. The contributors are experts in the discipline of actually getting global optimization to work, and the book provides a source of ideas for people needing to implement global optimization software.

Lectures on Convex Optimization

Author : Yurii Nesterov
Publisher : Springer
ISBN 13 : 3319915789
Total Pages : 589 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis Lectures on Convex Optimization by : Yurii Nesterov

Download or read book Lectures on Convex Optimization written by Yurii Nesterov and published by Springer. This book was released on 2018-11-19 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive, modern introduction to convex optimization, a field that is becoming increasingly important in applied mathematics, economics and finance, engineering, and computer science, notably in data science and machine learning. Written by a leading expert in the field, this book includes recent advances in the algorithmic theory of convex optimization, naturally complementing the existing literature. It contains a unified and rigorous presentation of the acceleration techniques for minimization schemes of first- and second-order. It provides readers with a full treatment of the smoothing technique, which has tremendously extended the abilities of gradient-type methods. Several powerful approaches in structural optimization, including optimization in relative scale and polynomial-time interior-point methods, are also discussed in detail. Researchers in theoretical optimization as well as professionals working on optimization problems will find this book very useful. It presents many successful examples of how to develop very fast specialized minimization algorithms. Based on the author’s lectures, it can naturally serve as the basis for introductory and advanced courses in convex optimization for students in engineering, economics, computer science and mathematics.

Convex Optimization Theory

Author : Dimitri Bertsekas
Publisher : Athena Scientific
ISBN 13 : 1886529310
Total Pages : 256 pages
Book Rating : 4.8/5 (865 download)

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Book Synopsis Convex Optimization Theory by : Dimitri Bertsekas

Download or read book Convex Optimization Theory written by Dimitri Bertsekas and published by Athena Scientific. This book was released on 2009-06-01 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: An insightful, concise, and rigorous treatment of the basic theory of convex sets and functions in finite dimensions, and the analytical/geometrical foundations of convex optimization and duality theory. Convexity theory is first developed in a simple accessible manner, using easily visualized proofs. Then the focus shifts to a transparent geometrical line of analysis to develop the fundamental duality between descriptions of convex functions in terms of points, and in terms of hyperplanes. Finally, convexity theory and abstract duality are applied to problems of constrained optimization, Fenchel and conic duality, and game theory to develop the sharpest possible duality results within a highly visual geometric framework. This on-line version of the book, includes an extensive set of theoretical problems with detailed high-quality solutions, which significantly extend the range and value of the book. The book may be used as a text for a theoretical convex optimization course; the author has taught several variants of such a course at MIT and elsewhere over the last ten years. It may also be used as a supplementary source for nonlinear programming classes, and as a theoretical foundation for classes focused on convex optimization models (rather than theory). It is an excellent supplement to several of our books: Convex Optimization Algorithms (Athena Scientific, 2015), Nonlinear Programming (Athena Scientific, 2017), Network Optimization(Athena Scientific, 1998), Introduction to Linear Optimization (Athena Scientific, 1997), and Network Flows and Monotropic Optimization (Athena Scientific, 1998).

Global Optimization

Author : Marco Locatelli
Publisher : SIAM
ISBN 13 : 1611972671
Total Pages : 439 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis Global Optimization by : Marco Locatelli

Download or read book Global Optimization written by Marco Locatelli and published by SIAM. This book was released on 2013-10-16 with total page 439 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains a thorough overview of the rapidly growing field of global optimization, with chapters on key topics such as complexity, heuristic methods, derivation of lower bounds for minimization problems, and branch-and-bound methods and convergence. The final chapter offers both benchmark test problems and applications of global optimization, such as finding the conformation of a molecule or planning an optimal trajectory for interplanetary space travel. An appendix provides fundamental information on convex and concave functions. Intended for Ph.D. students, researchers, and practitioners looking for advanced solution methods to difficult optimization problems. It can be used as a supplementary text in an advanced graduate-level seminar.

Convex Analysis for Optimization

Author : Jan Brinkhuis
Publisher : Springer Nature
ISBN 13 : 3030418049
Total Pages : 278 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Convex Analysis for Optimization by : Jan Brinkhuis

Download or read book Convex Analysis for Optimization written by Jan Brinkhuis and published by Springer Nature. This book was released on 2020-05-05 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers graduate students a concise introduction to the classic notions of convex optimization. Written in a highly accessible style and including numerous examples and illustrations, it presents everything readers need to know about convexity and convex optimization. The book introduces a systematic three-step method for doing everything, which can be summarized as "conify, work, deconify". It starts with the concept of convex sets, their primal description, constructions, topological properties and dual description, and then moves on to convex functions and the fundamental principles of convex optimization and their use in the complete analysis of convex optimization problems by means of a systematic four-step method. Lastly, it includes chapters on alternative formulations of optimality conditions and on illustrations of their use. "The author deals with the delicate subjects in a precise yet light-minded spirit... For experts in the field, this book not only offers a unifying view, but also opens a door to new discoveries in convexity and optimization...perfectly suited for classroom teaching." Shuzhong Zhang, Professor of Industrial and Systems Engineering, University of Minnesota

Lectures on Modern Convex Optimization

Author : Aharon Ben-Tal
Publisher : SIAM
ISBN 13 : 0898714915
Total Pages : 500 pages
Book Rating : 4.8/5 (987 download)

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Book Synopsis Lectures on Modern Convex Optimization by : Aharon Ben-Tal

Download or read book Lectures on Modern Convex Optimization written by Aharon Ben-Tal and published by SIAM. This book was released on 2001-01-01 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: Here is a book devoted to well-structured and thus efficiently solvable convex optimization problems, with emphasis on conic quadratic and semidefinite programming. The authors present the basic theory underlying these problems as well as their numerous applications in engineering, including synthesis of filters, Lyapunov stability analysis, and structural design. The authors also discuss the complexity issues and provide an overview of the basic theory of state-of-the-art polynomial time interior point methods for linear, conic quadratic, and semidefinite programming. The book's focus on well-structured convex problems in conic form allows for unified theoretical and algorithmical treatment of a wide spectrum of important optimization problems arising in applications.

Essays and Surveys in Global Optimization

Author : Charles Audet
Publisher : Springer Science & Business Media
ISBN 13 : 9780387255699
Total Pages : 314 pages
Book Rating : 4.2/5 (556 download)

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Book Synopsis Essays and Surveys in Global Optimization by : Charles Audet

Download or read book Essays and Surveys in Global Optimization written by Charles Audet and published by Springer Science & Business Media. This book was released on 2005-04-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global optimization aims at solving the most general problems of deterministic mathematical programming: to find the global optimum of a nonlinear, nonconvex, multivariate function of continuous and/or integer variables subject to constraints which may be themselves nonlinear and nonconvex. In addition, once the solutions are found, proof of its optimality is also expected from this methodology. Therefore, with these difficulties in mind, global optimization is becoming an increasingly powerful and important methodology. Essays and Surveys in Global Optimization is the most recent examination of its mathematical capability, power, and wide ranging solutions to many fields in the applied sciences.