Advances In Convex Analysis And Global Optimization

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Advances in Convex Analysis and Global Optimization

Nicolas Hadjisavvas,Panos M. Pardalos
Advances in Convex Analysis and Global Optimization Book PDF

Author : Nicolas Hadjisavvas,Panos M. Pardalos
Publisher : Springer Science & Business Media
Page : 601 pages
File Size : 42,5 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461302797

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Advances in Convex Analysis and Global Optimization by Nicolas Hadjisavvas,Panos M. Pardalos Pdf

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 Global Optimization

Hoang Tuy
Convex Analysis and Global Optimization Book PDF

Author : Hoang Tuy
Publisher : Springer
Page : 505 pages
File Size : 41,9 Mb
Release : 2016-10-17
Category : Mathematics
ISBN : 9783319314846

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Convex Analysis and Global Optimization by Hoang Tuy Pdf

This book presents state-of-the-art results and methodologies in modern global optimization, and has been a staple reference for researchers, engineers, advanced students (also in applied mathematics), and practitioners in various fields of engineering. The second edition has been brought up to date and continues to develop a coherent and rigorous theory of deterministic global optimization, highlighting the essential role of convex analysis. The text has been revised and expanded to meet the needs of research, education, and applications for many years to come. Updates for this new edition include: · Discussion of modern approaches to minimax, fixed point, and equilibrium theorems, and to nonconvex optimization; · Increased focus on dealing more efficiently with ill-posed problems of global optimization, particularly those with hard constraints; · Important discussions of decomposition methods for specially structured problems; · A complete revision of the chapter on nonconvex quadratic programming, in order to encompass the advances made in quadratic optimization since publication of the first edition. · Additionally, this new edition contains entirely new chapters devoted to monotonic optimization, polynomial optimization and optimization under equilibrium constraints, including bilevel programming, multiobjective programming, and optimization with variational inequality constraint. From the reviews of the first edition: The book gives a good review of the topic. ...The text is carefully constructed and well written, the exposition is clear. It leaves a remarkable impression of the concepts, tools and techniques in global optimization. It might also be used as a basis and guideline for lectures on this subject. Students as well as professionals will profitably read and use it.—Mathematical Methods of Operations Research, 49:3 (1999)

Advances in Global Optimization

David Gao,Ning Ruan,Wenxun Xing
Advances in Global Optimization Book PDF

Author : David Gao,Ning Ruan,Wenxun Xing
Publisher : Springer
Page : 537 pages
File Size : 52,8 Mb
Release : 2014-11-11
Category : Mathematics
ISBN : 9783319083773

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Advances in Global Optimization by David Gao,Ning Ruan,Wenxun Xing Pdf

This proceedings volume addresses advances in global optimization—a multidisciplinary research field that deals with the analysis, characterization and computation of global minima and/or maxima of nonlinear, non-convex and nonsmooth functions in continuous or discrete forms. The volume contains selected papers from the third biannual World Congress on Global Optimization in Engineering & Science (WCGO), held in the Yellow Mountains, Anhui, China on July 8-12, 2013. The papers fall into eight topical sections: mathematical programming; combinatorial optimization; duality theory; topology optimization; variational inequalities and complementarity problems; numerical optimization; stochastic models and simulation and complex simulation and supply chain analysis.

Abstract Convexity and Global Optimization

Alexander M. Rubinov
Abstract Convexity and Global Optimization Book PDF

Author : Alexander M. Rubinov
Publisher : Springer Science & Business Media
Page : 506 pages
File Size : 49,7 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9781475732009

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Abstract Convexity and Global Optimization by Alexander M. Rubinov Pdf

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.

Advances in Applied Mathematics and Global Optimization

David Y. Gao,Hanif D. Sherali
Advances in Applied Mathematics and Global Optimization Book PDF

Author : David Y. Gao,Hanif D. Sherali
Publisher : Springer Science & Business Media
Page : 520 pages
File Size : 45,8 Mb
Release : 2009-04-09
Category : Mathematics
ISBN : 9780387757148

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Advances in Applied Mathematics and Global Optimization by David Y. Gao,Hanif D. Sherali Pdf

The articles that comprise this distinguished annual volume for the Advances in Mechanics and Mathematics series have been written in honor of Gilbert Strang, a world renowned mathematician and exceptional person. Written by leading experts in complementarity, duality, global optimization, and quantum computations, this collection reveals the beauty of these mathematical disciplines and investigates recent developments in global optimization, nonconvex and nonsmooth analysis, nonlinear programming, theoretical and engineering mechanics, large scale computation, quantum algorithms and computation, and information theory.

Global Optimization

Leo Liberti,Nelson Maculan
Global Optimization Book PDF

Author : Leo Liberti,Nelson Maculan
Publisher : Springer Science & Business Media
Page : 454 pages
File Size : 41,7 Mb
Release : 2006-02-21
Category : Business & Economics
ISBN : 0387282602

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Global Optimization by Leo Liberti,Nelson Maculan Pdf

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.

Advances in Stochastic and Deterministic Global Optimization

Panos M. Pardalos,Anatoly Zhigljavsky,Julius Žilinskas
Advances in Stochastic and Deterministic Global Optimization Book PDF

Author : Panos M. Pardalos,Anatoly Zhigljavsky,Julius Žilinskas
Publisher : Springer
Page : 296 pages
File Size : 45,6 Mb
Release : 2016-11-04
Category : Mathematics
ISBN : 9783319299754

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Advances in Stochastic and Deterministic Global Optimization by Panos M. Pardalos,Anatoly Zhigljavsky,Julius Žilinskas Pdf

Current research results in stochastic and deterministic global optimization including single and multiple objectives are explored and presented in this book by leading specialists from various fields. Contributions include applications to multidimensional data visualization, regression, survey calibration, inventory management, timetabling, chemical engineering, energy systems, and competitive facility location. Graduate students, researchers, and scientists in computer science, numerical analysis, optimization, and applied mathematics will be fascinated by the theoretical, computational, and application-oriented aspects of stochastic and deterministic global optimization explored in this book. This volume is dedicated to the 70th birthday of Antanas Žilinskas who is a leading world expert in global optimization. Professor Žilinskas's research has concentrated on studying models for the objective function, the development and implementation of efficient algorithms for global optimization with single and multiple objectives, and application of algorithms for solving real-world practical problems.

Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming

Mohit Tawarmalani,Nikolaos V. Sahinidis
Convexification and Global Optimization in Continuous and Mixed Integer Nonlinear Programming Book PDF

Author : Mohit Tawarmalani,Nikolaos V. Sahinidis
Publisher : Springer Science & Business Media
Page : 492 pages
File Size : 42,5 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475735321

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Convexification and Global Optimization in Continuous and Mixed-Integer Nonlinear Programming by Mohit Tawarmalani,Nikolaos V. Sahinidis Pdf

Interest in constrained optimization originated with the simple linear pro gramming model since it was practical and perhaps the only computationally tractable model at the time. Constrained linear optimization models were soon adopted in numerous application areas and are perhaps the most widely used mathematical models in operations research and management science at the time of this writing. Modelers have, however, found the assumption of linearity to be overly restrictive in expressing the real-world phenomena and problems in economics, finance, business, communication, engineering design, computational biology, and other areas that frequently demand the use of nonlinear expressions and discrete variables in optimization models. Both of these extensions of the linear programming model are NP-hard, thus representing very challenging problems. On the brighter side, recent advances in algorithmic and computing technology make it possible to re visit these problems with the hope of solving practically relevant problems in reasonable amounts of computational time. Initial attempts at solving nonlinear programs concentrated on the de velopment of local optimization methods guaranteeing globality under the assumption of convexity. On the other hand, the integer programming liter ature has concentrated on the development of methods that ensure global optima. The aim of this book is to marry the advancements in solving nonlinear and integer programming models and to develop new results in the more general framework of mixed-integer nonlinear programs (MINLPs) with the goal of devising practically efficient global optimization algorithms for MINLPs.

Recent Advances in Optimization

Peter Gritzmann,Reiner Horst,Ekkehard Sachs,Rainer Tichatschke
Recent Advances in Optimization Book PDF

Author : Peter Gritzmann,Reiner Horst,Ekkehard Sachs,Rainer Tichatschke
Publisher : Springer Science & Business Media
Page : 388 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642590733

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Recent Advances in Optimization by Peter Gritzmann,Reiner Horst,Ekkehard Sachs,Rainer Tichatschke Pdf

This book presents recent theoretical and practical aspects in the field of optimization and convex analysis. The topics covered in this volume include: - Equilibrium models in economics. - Control theory and semi-infinite programming. - Ill-posed variational problems. - Global optimization. - Variational methods in image restoration. - Nonsmooth optimization. - Duality theory in convex and nonconvex optimization. - Methods for large scale problems.

Recent Advances in Global Optimization

Christodoulos A. Floudas,Panos M. Pardalos
Recent Advances in Global Optimization Book PDF

Author : Christodoulos A. Floudas,Panos M. Pardalos
Publisher : Princeton University Press
Page : 644 pages
File Size : 54,9 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781400862528

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Recent Advances in Global Optimization by Christodoulos A. Floudas,Panos M. Pardalos Pdf

This book will present the papers delivered at the first U.S. conference devoted exclusively to global optimization and will thus provide valuable insights into the significant research on the topic that has been emerging during recent years. Held at Princeton University in May 1991, the conference brought together an interdisciplinary group of the most active developers of algorithms for global optimization in order to focus the attention of the mathematical programming community on the unsolved problems and diverse applications of this field. The main subjects addressed at the conference were advances in deterministic and stochastic methods for global optimization, parallel algorithms for global optimization problems, and applications of global optimization. Although global optimization is primarily a mathematical problem, it is relevant to several other disciplines, including computer science, applied mathematics, physical chemistry, molecular biology, statistics, physics, engineering, operations research, communication theory, and economics. Global optimization problems originate from a wide variety of mathematical models of real-world systems. Some of its applications are allocation and location problems and VLSI and data-base design problems. Originally published in 1991. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Essays and Surveys in Global Optimization

Charles Audet,Pierre Hansen,Giles Savard
Essays and Surveys in Global Optimization Book PDF

Author : Charles Audet,Pierre Hansen,Giles Savard
Publisher : Springer Science & Business Media
Page : 314 pages
File Size : 55,8 Mb
Release : 2005-04-20
Category : Business & Economics
ISBN : 0387255699

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Essays and Surveys in Global Optimization by Charles Audet,Pierre Hansen,Giles Savard Pdf

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.

Lectures on Convex Optimization

Yurii Nesterov
Lectures on Convex Optimization Book PDF

Author : Yurii Nesterov
Publisher : Springer
Page : 589 pages
File Size : 53,9 Mb
Release : 2018-11-19
Category : Mathematics
ISBN : 9783319915784

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Lectures on Convex Optimization by Yurii Nesterov Pdf

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.

Progress in Optimization

Andrew Eberhard,Robin Hill,Daniel Ralph,Barney M. Glover
Progress in Optimization Book PDF

Author : Andrew Eberhard,Robin Hill,Daniel Ralph,Barney M. Glover
Publisher : Springer Science & Business Media
Page : 309 pages
File Size : 48,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461332855

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Progress in Optimization by Andrew Eberhard,Robin Hill,Daniel Ralph,Barney M. Glover Pdf

Although the monograph Progress in Optimization I: Contributions from Aus tralasia grew from the idea of publishing a proceedings of the Fourth Optimiza tion Day, held in July 1997 at the Royal Melbourne Institute of Technology, the focus soon changed to a refereed volume in optimization. The intention is to publish a similar book annually, following each Optimization Day. The idea of having an annual Optimization Day was conceived by Barney Glover; the first of these Optimization Days was held in 1994 at the University of Ballarat. Barney hoped that such a yearly event would bring together the many, but widely dispersed, researchers in Australia who were publishing in optimization and related areas such as control. The first Optimization Day event was followed by similar conferences at The University of New South Wales (1995), The University of Melbourne (1996), the Royal Melbourne Institute of Technology (1997), and The University of Western Australia (1998). The 1999 conference will return to Ballarat University, being organized by Barney's long-time collaborator Alex Rubinov. In recent years the Optimization Day has been held in conjunction with other locally-held national or international conferences. This has widened the scope of the monograph with contributions not only coming from researchers in Australia and neighboring regions but also from their collaborators in Europe and North America.

Introduction to Global Optimization

R. Horst,Panos M. Pardalos,Nguyen Van Thoai
Introduction to Global Optimization Book PDF

Author : R. Horst,Panos M. Pardalos,Nguyen Van Thoai
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 55,8 Mb
Release : 2000-12-31
Category : Computers
ISBN : 0792367561

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Introduction to Global Optimization by R. Horst,Panos M. Pardalos,Nguyen Van Thoai Pdf

A textbook for an undergraduate course in mathematical programming for students with a knowledge of elementary real analysis, linear algebra, and classical linear programming (simple techniques). Focuses on the computation and characterization of global optima of nonlinear functions, rather than the locally optimal solutions addressed by most books on optimization. Incorporates the theoretical, algorithmic, and computational advances of the past three decades that help solve globally multi-extreme problems in the mathematical modeling of real world systems. Annotation copyright by Book News, Inc., Portland, OR

Variational Analysis and Set Optimization

Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer
Variational Analysis and Set Optimization Book PDF

Author : Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer
Publisher : CRC Press
Page : 226 pages
File Size : 45,7 Mb
Release : 2019-06-07
Category : Business & Economics
ISBN : 9781351712064

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Variational Analysis and Set Optimization by Akhtar A. Khan,Elisabeth Köbis,Christiane Tammer Pdf

This book contains the latest advances in variational analysis and set / vector optimization, including uncertain optimization, optimal control and bilevel optimization. Recent developments concerning scalarization techniques, necessary and sufficient optimality conditions and duality statements are given. New numerical methods for efficiently solving set optimization problems are provided. Moreover, applications in economics, finance and risk theory are discussed. Summary The objective of this book is to present advances in different areas of variational analysis and set optimization, especially uncertain optimization, optimal control and bilevel optimization. Uncertain optimization problems will be approached from both a stochastic as well as a robust point of view. This leads to different interpretations of the solutions, which widens the choices for a decision-maker given his preferences. Recent developments regarding linear and nonlinear scalarization techniques with solid and nonsolid ordering cones for solving set optimization problems are discussed in this book. These results are useful for deriving optimality conditions for set and vector optimization problems. Consequently, necessary and sufficient optimality conditions are presented within this book, both in terms of scalarization as well as generalized derivatives. Moreover, an overview of existing duality statements and new duality assertions is given. The book also addresses the field of variable domination structures in vector and set optimization. Including variable ordering cones is especially important in applications such as medical image registration with uncertainties. This book covers a wide range of applications of set optimization. These range from finance, investment, insurance, control theory, economics to risk theory. As uncertain multi-objective optimization, especially robust approaches, lead to set optimization, one main focus of this book is uncertain optimization. Important recent developments concerning numerical methods for solving set optimization problems sufficiently fast are main features of this book. These are illustrated by various examples as well as easy-to-follow-steps in order to facilitate the decision process for users. Simple techniques aimed at practitioners working in the fields of mathematical programming, finance and portfolio selection are presented. These will help in the decision-making process, as well as give an overview of nondominated solutions to choose from.