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Invexity And Optimization

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Invexity And Optimization

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Author : Shashi K. Mishra
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-23

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 2008-05-23 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.

Invexity And Optimization

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

Continuous Optimization And Variational Inequalities

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Author : Anurag Jayswal
language : en
Publisher: CRC Press
Release Date : 2022-09-13

Continuous Optimization And Variational Inequalities written by Anurag Jayswal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-13 with Technology & Engineering categories.

The proposed book provides a comprehensive coverage of theory and methods in the areas of continuous optimization and variational inequality. It describes theory and solution methods for optimization with smooth and non-smooth functions, for variational inequalities with single-valued and multivalued mappings, and for related classes such as mixed variational inequalities, complementarity problems, and general equilibrium problems. The emphasis is made on revealing generic properties of these problems that allow creation of efficient solution methods. Salient Features The book presents a deep, wide-ranging introduction to the theory of the optimal control of processes governed by optimization techniques and variational inequality Several solution methods are provided which will help the reader to develop various optimization tools for real-life problems which can be modeled by optimization techniques involving linear and nonlinear functions. The book focuses on most recent contributions in the nonlinear phenomena, which can appear in various areas of human activities. This book also presents relevant mathematics clearly and simply to help solve real life problems in diverse fields such as mechanical engineering, management, control behavior, traffic signal, industry, etc. This book is aimed primarily at advanced undergraduates and graduate students pursuing computer engineering and electrical engineering courses. Researchers, academicians and industry people will also find this book useful.

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

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

Generalized Convexity written by Sandor Komlosi 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 Business & Economics categories.

Generalizations of the classical concept of a convex function have been proposed in various fields such as economics, management science, engineering, statistics and applied sciences during the second half of this century. In addition to new results in more established areas of generalized convexity, this book presents several important developments in recently emerging areas. Also, a number of interesting applications are reported.

Variational Analysis With Applications In Optimisation And Control

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Author : Savin Treanţă
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2019-08-01

Variational Analysis With Applications In Optimisation And Control written by Savin Treanţă and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-08-01 with Mathematics categories.

This book focuses on the calculus of variations and related applications which combine tools and methods from partial differential equations with geometrical techniques. More precisely, it is devoted to nonlinear problems coming from different areas, with particular reference to those introducing new techniques capable of solving a wide range of problems. It provides the latest developments in multidimensional optimization and optimal control. With various examples and applications to complement and substantiate mathematical developments, the text is a valuable guide for researchers, engineers and students in the field of mathematics, and those working in operations research, optimal control science, artificial intelligence, management science and economics.

Generalized Convexity And Vector Optimization

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Author : Shashi K. Mishra
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-19

Generalized Convexity And Vector 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 2008-12-19 with Mathematics categories.

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.

Encyclopedia Of Optimization

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Author : Christodoulos A. Floudas
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-09-04

Encyclopedia Of Optimization written by Christodoulos A. Floudas 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 2008-09-04 with Mathematics categories.

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".

V Invex Functions And Vector Optimization

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Author : Shashi K. Mishra
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-11-17

V Invex Functions And Vector 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 2007-11-17 with Mathematics categories.

This volume summarizes and synthesizes an aspect of research work that has been done in the area of Generalized Convexity over the past few decades. Specifically, the book focuses on V-invex functions in vector optimization that have grown out of the work of Jeyakumar and Mond in the 1990’s. The authors integrate related research into the book and demonstrate the wide context from which the area has grown and continues to grow.

Optimization In Economics And Finance

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Author : Bruce D. Craven
language : en
Publisher: Springer
Release Date : 2011-01-05

Optimization In Economics And Finance written by Bruce D. Craven and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-05 with Business & Economics categories.

Some recent developments in the mathematics of optimization, including the concepts of invexity and quasimax, have not yet been applied to models of economic growth, and to finance and investment. Their applications to these areas are shown in this book.

Invexity And Optimization

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