**Author**: C.j. Goh

**Publisher:**Taylor & Francis

**ISBN:**9780415274791

**Size**: 22.22 MB

**Format:**PDF, Kindle

**Category :**Mathematics

**Languages :**un

**Pages :**336

**View:**5355

**Book Description:**This comprehensive volume covers a wide range of duality topics ranging from simple ideas in network flows to complex issues in non-convex optimization and multicriteria problems. In addition, it examines duality in the context of variational inequalities and vector variational inequalities, as generalizations to optimization. Duality in Optimization and Variational Inequalities is intended for researchers and practitioners of optimization with the aim of enhancing their understanding of duality. It provides a wider appreciation of optimality conditions in various scenarios and under different assumptions. It will enable the reader to use duality to devise more effective computational methods, and to aid more meaningful interpretation of optimization and variational inequality problems.

## A Duality Approach To Gap Functions For Variational Inequalities And Equilibrium Problems

**Author**:

**Publisher:**

**ISBN:**

**Size**: 59.76 MB

**Format:**PDF

**Category :**

**Languages :**un

**Pages :**

**View:**5349

**Book Description:**This work aims to investigate some applications of the conjugate duality for scalar and vector optimization problems to the construction of gap functions for variational inequalities and equilibrium problems. The basic idea of the approach is to reformulate variational inequalities and equilibrium problems into optimization problems depending on a fixed variable, which allows us to apply duality results from optimization problems. Based on some perturbations, first we consider the conjugate duality for scalar optimization. As applications, duality investigations for the convex partially separable optimization problem are discussed. Afterwards, we concentrate our attention on some applications of conjugate duality for convex optimization problems in finite and infinite-dimensional spaces to the construction of a gap function for variational inequalities and equilibrium problems. To verify the properties in the definition of a gap function weak and strong duality are used. The remainder of this thesis deals with the extension of this approach to vector variational inequalities and vector equilibrium problems. By using the perturbation functions in analogy to the scalar case, different dual problems for vector optimization and duality assertions for these problems are derived. This study allows us to propose some set-valued gap functions for the vector variational inequality. Finally, by applying the Fenchel duality on the basis of weak orderings, some variational principles for vector equilibrium problems are investigated.

## Contributions To The Theory Of Variational Inequalities Equilibrium And Optimization Problems Via Duality

**Author**: Liana Cioban

**Publisher:**

**ISBN:**

**Size**: 26.46 MB

**Format:**PDF, ePub, Docs

**Category :**

**Languages :**un

**Pages :**262

**View:**1476

**Book Description:**

## Asymptotic Cones And Functions In Optimization And Variational Inequalities

**Author**: Alfred Auslender

**Publisher:**Springer Science & Business Media

**ISBN:**0387955208

**Size**: 55.98 MB

**Format:**PDF, Docs

**Category :**Mathematics

**Languages :**un

**Pages :**249

**View:**3352

**Book Description:**This systematic and comprehensive account of asymptotic sets and functions develops a broad and useful theory in the areas of optimization and variational inequalities. The central focus is on problems of handling unbounded situations, using solutions of a given problem in these classes, when for example standard compacity hypothesis is not present. This book will interest advanced graduate students, researchers, and practitioners of optimization theory, nonlinear programming, and applied mathematics.

## Advances In Global Optimization

**Author**: David Gao

**Publisher:**Springer

**ISBN:**3319083775

**Size**: 56.94 MB

**Format:**PDF, Docs

**Category :**Mathematics

**Languages :**un

**Pages :**537

**View:**6959

**Book Description:**This proceedings volume addresses advances in global optimizationâ€”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.

## Journal Of Nonlinear And Convex Analysis

**Author**:

**Publisher:**

**ISBN:**

**Size**: 15.41 MB

**Format:**PDF, Mobi

**Category :**Convex domains

**Languages :**en

**Pages :**

**View:**2834

**Book Description:**

## Conjugate Duality In Vector Optimization And Some Applications To The Vector Variational Inequality

**Author**: Altangerel Lkhamsuren

**Publisher:**

**ISBN:**

**Size**: 47.24 MB

**Format:**PDF, Mobi

**Category :**

**Languages :**un

**Pages :**31

**View:**1269

**Book Description:**

## Mathematical Reviews

**Author**:

**Publisher:**

**ISBN:**

**Size**: 52.27 MB

**Format:**PDF

**Category :**Mathematics

**Languages :**en

**Pages :**

**View:**1530

**Book Description:**

## Optimization And Control With Applications

**Author**: Liqun Qi

**Publisher:**Springer Science & Business Media

**ISBN:**0387242554

**Size**: 46.42 MB

**Format:**PDF, Kindle

**Category :**Mathematics

**Languages :**un

**Pages :**562

**View:**1464

**Book Description:**A collection of 28 refereed papers grouped according to four broad topics: duality and optimality conditions, optimization algorithms, optimal control, and variational inequality and equilibrium problems. Suitable for researchers, practitioners and postgrads.

## Generalized Convexity And Vector Optimization

**Author**: Shashi K. Mishra

**Publisher:**Springer Science & Business Media

**ISBN:**3540856714

**Size**: 19.86 MB

**Format:**PDF, Mobi

**Category :**Mathematics

**Languages :**un

**Pages :**294

**View:**2052

**Book Description:**The present lecture note is dedicated to the study of the optimality conditions and the duality results for nonlinear vector optimization problems, in ?nite and in?nite dimensions. The problems include are nonlinear vector optimization problems, s- metric dual problems, continuous-time vector optimization problems, relationships between vector optimization and variational inequality problems. Nonlinear vector optimization problems arise in several contexts such as in the building and interpretation of economic models; the study of various technolo- cal processes; the development of optimal choices in ?nance; management science; production processes; transportation problems and statistical decisions, etc. In preparing this lecture note a special effort has been made to obtain a se- contained treatment of the subjects; so we hope that this may be a suitable source for a beginner in this fast growing area of research, a semester graduate course in nonlinear programing, and a good reference book. This book may be useful to theoretical economists, engineers, and applied researchers involved in this area of active research. The lecture note is divided into eight chapters: Chapter 1 brie?y deals with the notion of nonlinear programing problems with basic notations and preliminaries. Chapter 2 deals with various concepts of convex sets, convex functions, invex set, invex functions, quasiinvex functions, pseudoinvex functions, type I and generalized type I functions, V-invex functions, and univex functions.