Combined Relaxation Methods for Variational Inequalities
Combined Relaxation Methods for Variational Inequalities

Author: Igor Konnov

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 190

ISBN-13: 3642568866

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Variational inequalities proved to be a very useful and powerful tool for in vestigation and solution of many equilibrium type problems in Economics, Engineering, Operations Research and Mathematical Physics. In fact, varia tional inequalities for example provide a unifying framework for the study of such diverse problems as boundary value problems, price equilibrium prob lems and traffic network equilibrium problems. Besides, they are closely re lated with many general problems of Nonlinear Analysis, such as fixed point, optimization and complementarity problems. As a result, the theory and so lution methods for variational inequalities have been studied extensively, and considerable advances have been made in these areas. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relax ation (CR) approach. This approach is based on combining, modifying and generalizing ideas contained in various relaxation methods. In fact, each com bined relaxation method has a two-level structure, i.e., a descent direction and a stepsize at each iteration are computed by finite relaxation procedures.

Generalized Convexity and Related Topics
Generalized Convexity and Related Topics

Author: Igor V. Konnov

Publisher: Springer Science & Business Media

Published: 2006-11-22

Total Pages: 465

ISBN-13: 3540370072

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The book contains invited papers by well-known experts on a wide range of topics (economics, variational analysis, probability etc.) closely related to convexity and generalized convexity, and refereed contributions of specialists from the world on current research on generalized convexity and applications, in particular, to optimization, economics and operations research.

Encyclopedia of Optimization
Encyclopedia of Optimization

Author: Christodoulos A. Floudas

Publisher: Springer Science & Business Media

Published: 2008-09-04

Total Pages: 4646

ISBN-13: 0387747583

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The goal of the Encyclopedia of Optimization is to introduce the reader to a complete set of topics that show the spectrum of research, the richness of ideas, and the breadth of applications that has come from this field. The second edition builds on the success of the former edition with more than 150 completely new entries, designed to ensure that the reference addresses recent areas where optimization theories and techniques have advanced. Particularly heavy attention resulted in health science and transportation, with entries such as "Algorithms for Genomics", "Optimization and Radiotherapy Treatment Design", and "Crew Scheduling".

Uncertainty Quantification in Variational Inequalities
Uncertainty Quantification in Variational Inequalities

Author: Joachim Gwinner

Publisher: CRC Press

Published: 2021-12-21

Total Pages: 334

ISBN-13: 1351857665

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Uncertainty Quantification (UQ) is an emerging and extremely active research discipline which aims to quantitatively treat any uncertainty in applied models. The primary objective of Uncertainty Quantification in Variational Inequalities: Theory, Numerics, and Applications is to present a comprehensive treatment of UQ in variational inequalities and some of its generalizations emerging from various network, economic, and engineering models. Some of the developed techniques also apply to machine learning, neural networks, and related fields. Features First book on UQ in variational inequalities emerging from various network, economic, and engineering models Completely self-contained and lucid in style Aimed for a diverse audience including applied mathematicians, engineers, economists, and professionals from academia Includes the most recent developments on the subject which so far have only been available in the research literature

Handbook of Generalized Convexity and Generalized Monotonicity
Handbook of Generalized Convexity and Generalized Monotonicity

Author: Nicolas Hadjisavvas

Publisher: Springer Science & Business Media

Published: 2006-01-16

Total Pages: 684

ISBN-13: 0387233938

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Studies in generalized convexity and generalized monotonicity have significantly increased during the last two decades. Researchers with very diverse backgrounds such as mathematical programming, optimization theory, convex analysis, nonlinear analysis, nonsmooth analysis, linear algebra, probability theory, variational inequalities, game theory, economic theory, engineering, management science, equilibrium analysis, for example are attracted to this fast growing field of study. Such enormous research activity is partially due to the discovery of a rich, elegant and deep theory which provides a basis for interesting existing and potential applications in different disciplines. The handbook offers an advanced and broad overview of the current state of the field. It contains fourteen chapters written by the leading experts on the respective subject; eight on generalized convexity and the remaining six on generalized monotonicity.

Combined Relaxation Methods for Variational Inequalities
Combined Relaxation Methods for Variational Inequalities

Author: Igor Konnov

Publisher: Springer

Published: 2011-04-27

Total Pages: 200

ISBN-13: 9783642568879

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Variational inequalities proved to be a very useful tool for investigation and solution of various equilibrium type problems arising in Economics, Operations Research, Mathematical Physics, and Transportation. This book is devoted to a new general approach to constructing solution methods for variational inequalities, which was called the combined relaxation approach. This approach is rather flexible and allows one to construct various methods both for single-valued and for multi-valued variational inequalities, including nonlinear constrained problems. The other essential feature of the combined relaxation methods is that they are convergent under very mild assumptions. The book can be viewed as an attempt to discribe the existing combined relaxation methods as a whole.

Vector Variational Inequalities and Vector Optimization
Vector Variational Inequalities and Vector Optimization

Author: Qamrul Hasan Ansari

Publisher: Springer

Published: 2017-10-31

Total Pages: 517

ISBN-13: 3319630490

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This book presents the mathematical theory of vector variational inequalities and their relations with vector optimization problems. It is the first-ever book to introduce well-posedness and sensitivity analysis for vector equilibrium problems. The first chapter provides basic notations and results from the areas of convex analysis, functional analysis, set-valued analysis and fixed-point theory for set-valued maps, as well as a brief introduction to variational inequalities and equilibrium problems. Chapter 2 presents an overview of analysis over cones, including continuity and convexity of vector-valued functions. The book then shifts its focus to solution concepts and classical methods in vector optimization. It describes the formulation of vector variational inequalities and their applications to vector optimization, followed by separate chapters on linear scalarization, nonsmooth and generalized vector variational inequalities. Lastly, the book introduces readers to vector equilibrium problems and generalized vector equilibrium problems. Written in an illustrative and reader-friendly way, the book offers a valuable resource for all researchers whose work involves optimization and vector optimization.

Finite-Dimensional Variational Inequalities and Complementarity Problems
Finite-Dimensional Variational Inequalities and Complementarity Problems

Author: Francisco Facchinei

Publisher: Springer Science & Business Media

Published: 2007-06-04

Total Pages: 698

ISBN-13: 0387218157

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This is part two of a two-volume work presenting a comprehensive treatment of the finite-dimensional variational inequality and complementarity problem. It details algorithms for solving finite dimensional variational inequalities and complementarity problems. Coverage includes abundant exercises as well as an extensive bibliography. The book will be an enduring reference on the subject and provide the foundation for its sustained growth.

Optimization Theory and Related Topics
Optimization Theory and Related Topics

Author: Simeon Reich

Publisher: American Mathematical Soc.

Published: 2012

Total Pages: 296

ISBN-13: 0821869086

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This volume contains the proceedings of the workshop on Optimization Theory and Related Topics, held in memory of Dan Butnariu, from January 11-14, 2010, in Haifa, Israel. An active researcher in various fields of applied mathematics, Butnariu published over 80 papers. His extensive bibliography is included in this volume. The articles in this volume cover many different areas of Optimization Theory and its applications: maximal monotone operators, sensitivity estimates via Lyapunov functions, inverse Newton transforms, infinite-horizon Pontryagin principles, singular optimal control problems with state delays, descent methods for mixed variational inequalities, games on MV-algebras, ergodic convergence in subgradient optimization, applications to economics and technology planning, the exact penalty property in constrained optimization, nonsmooth inverse problems, Bregman distances, retraction methods in Banach spaces, and iterative methods for solving equilibrium problems. This volume will be of interest to both graduate students and research mathematicians.

Recent Advances in Optimization
Recent Advances in Optimization

Author: Alberto Seeger

Publisher: Springer Science & Business Media

Published: 2006-01-26

Total Pages: 457

ISBN-13: 3540282580

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The contributions appearing in this book give an overview of recent research done in optimization and related areas, such as optimal control, calculus of variations, and game theory. They do not only address abstract issues of optimization theory, but are also concerned with the modeling and computer resolution of specific optimization problems arising in industry and applied sciences.