Generalized Convexity Generalized Monotonicity Recent Results

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Generalized Convexity Generalized Monotonicity Recent Results

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Author : Jean-Pierre Crouzeix
language : en
Publisher: Springer Science & Business Media
Release Date : 1998-08-31

Generalized Convexity Generalized Monotonicity Recent Results written by Jean-Pierre Crouzeix and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-08-31 with Mathematics categories.

A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems.

Generalized Convexity Generalized Monotonicity Recent Results

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Author : Jean-Pierre Crouzeix
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Generalized Convexity Generalized Monotonicity Recent Results written by Jean-Pierre Crouzeix and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.

A function is convex if its epigraph is convex. This geometrical structure has very strong implications in terms of continuity and differentiability. Separation theorems lead to optimality conditions and duality for convex problems. A function is quasiconvex if its lower level sets are convex. Here again, the geo metrical structure of the level sets implies some continuity and differentiability properties for quasiconvex functions. Optimality conditions and duality can be derived for optimization problems involving such functions as well. Over a period of about fifty years, quasiconvex and other generalized convex functions have been considered in a variety of fields including economies, man agement science, engineering, probability and applied sciences in accordance with the need of particular applications. During the last twenty-five years, an increase of research activities in this field has been witnessed. More recently generalized monotonicity of maps has been studied. It relates to generalized convexity off unctions as monotonicity relates to convexity. Generalized monotonicity plays a role in variational inequality problems, complementarity problems and more generally, in equilibrium prob lems.

Generalized Convexity Generalized Monotonicity And Applications

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Author : Andrew Eberhard
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-06-22

Generalized Convexity Generalized Monotonicity And Applications written by Andrew Eberhard and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-06-22 with Business & Economics categories.

In recent years there is a growing interest in generalized convex fu- tions and generalized monotone mappings among the researchers of - plied mathematics and other sciences. This is due to the fact that mathematical models with these functions are more suitable to describe problems of the real world than models using conventional convex and monotone functions. Generalized convexity and monotonicity are now considered as an independent branch of applied mathematics with a wide range of applications in mechanics, economics, engineering, finance and many others. The present volume contains 20 full length papers which reflect c- rent theoretical studies of generalized convexity and monotonicity, and numerous applications in optimization, variational inequalities, equil- rium problems etc. All these papers were refereed and carefully selected from invited talks and contributed talks that were presented at the 7th International Symposium on Generalized Convexity/Monotonicity held in Hanoi, Vietnam, August 27-31, 2002. This series of Symposia is or- nized by the Working Group on Generalized Convexity (WGGC) every 3 years and aims to promote and disseminate research on the field. The WGGC (http://www.genconv.org) consists of more than 300 researchers coming from 36 countries.

Handbook Of Generalized Convexity And Generalized Monotonicity

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Author : Nicolas Hadjisavvas
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-16

Handbook Of Generalized Convexity And Generalized Monotonicity written by Nicolas Hadjisavvas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-16 with Mathematics categories.

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.

Generalized Convexity And Generalized Monotonicity

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Author : Nicolas Hadjisavvas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Generalized Convexity And Generalized Monotonicity written by Nicolas Hadjisavvas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.

Various generalizations of convex functions have been introduced in areas such as mathematical programming, economics, management science, engineering, stochastics and applied sciences, for example. Such functions preserve one or more properties of convex functions and give rise to models which are more adaptable to real-world situations than convex models. Similarly, generalizations of monotone maps have been studied recently. A growing literature of this interdisciplinary field has appeared, and a large number of international meetings are entirely devoted or include clusters on generalized convexity and generalized monotonicity. The present book contains a selection of refereed papers presented at the 6th International Symposium on Generalized Convexity/Monotonicity, and aims to review the latest developments in the field.

Generalized Convexity And Optimization

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Author : Alberto Cambini
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-14

Generalized Convexity And Optimization written by Alberto Cambini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-10-14 with Mathematics categories.

The authors have written a rigorous yet elementary and self-contained book to present, in a unified framework, generalized convex functions. The book also includes numerous exercises and two appendices which list the findings consulted.

Optimality Conditions In Vector Optimization

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Author : Manuel Arana Jiménez
language : en
Publisher: Bentham Science Publishers
Release Date : 2010

Optimality Conditions In Vector Optimization written by Manuel Arana Jiménez and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.

Vector optimization is continuously needed in several science fields, particularly in economy, business, engineering, physics and mathematics. The evolution of these fields depends, in part, on the improvements in vector optimization in mathematical programming. The aim of this Ebook is to present the latest developments in vector optimization. The contributions have been written by some of the most eminent researchers in this field of mathematical programming. The Ebook is considered essential for researchers and students in this field.

Convex Analysis In General Vector Spaces

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Author : C. Zalinescu
language : en
Publisher: World Scientific
Release Date : 2002

Convex Analysis In General Vector Spaces written by C. Zalinescu and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.

The primary aim of this book is to present the conjugate and sub/differential calculus using the method of perturbation functions in order to obtain the most general results in this field. The secondary aim is to provide important applications of this calculus and of the properties of convex functions. Such applications are: the study of well-conditioned convex functions, uniformly convex and uniformly smooth convex functions, best approximation problems, characterizations of convexity, the study of the sets of weak sharp minima, well-behaved functions and the existence of global error bounds for convex inequalities, as well as the study of monotone multifunctions by using convex functions.

Invexity And Optimization

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Author : Shashi K. Mishra
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-24

Invexity And Optimization written by Shashi K. Mishra and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-24 with Mathematics categories.

Invexity and Optimization presents results on invex function and their properties in smooth and nonsmooth cases, pseudolinearity and eta-pseudolinearity. Results on optimality and duality for a nonlinear scalar programming problem are presented, second and higher order duality results are given for a nonlinear scalar programming problem, and saddle point results are also presented. Invexity in multiobjective programming problems and Kuhn-Tucker optimality conditions are given for a multiobjecive programming problem, Wolfe and Mond-Weir type dual models are given for a multiobjective programming problem and usual duality results are presented in presence of invex functions. Continuous-time multiobjective problems are also discussed. Quadratic and fractional programming problems are given for invex functions. Symmetric duality results are also given for scalar and vector cases.

Recent Advances In Nonsmooth Optimization

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Author : Ding-zhu Du
language : en
Publisher: World Scientific
Release Date : 1995-09-20

Recent Advances In Nonsmooth Optimization written by Ding-zhu Du and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-09-20 with Mathematics categories.

Nonsmooth optimization covers the minimization or maximization of functions which do not have the differentiability properties required by classical methods. The field of nonsmooth optimization is significant, not only because of the existence of nondifferentiable functions arising directly in applications, but also because several important methods for solving difficult smooth problems lead directly to the need to solve nonsmooth problems, which are either smaller in dimension or simpler in structure.This book contains twenty five papers written by forty six authors from twenty countries in five continents. It includes papers on theory, algorithms and applications for problems with first-order nondifferentiability (the usual sense of nonsmooth optimization) second-order nondifferentiability, nonsmooth equations, nonsmooth variational inequalities and other problems related to nonsmooth optimization.