Generalized Convexity And Generalized Monotonicity

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Handbook of Generalized Convexity and Generalized Monotonicity

Nicolas Hadjisavvas,Sándor Komlósi,Siegfried S. Schaible
Handbook of Generalized Convexity and Generalized Monotonicity Book PDF

Author : Nicolas Hadjisavvas,Sándor Komlósi,Siegfried S. Schaible
Publisher : Springer Science & Business Media
Page : 684 pages
File Size : 52,5 Mb
Release : 2006-01-16
Category : Mathematics
ISBN : 9780387233932

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Handbook of Generalized Convexity and Generalized Monotonicity by Nicolas Hadjisavvas,Sándor Komlósi,Siegfried S. Schaible Pdf

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, Generalized Monotonicity and Applications

Andrew Eberhard,Nicolas Hadjisavvas,D.T. Luc
Generalized Convexity Generalized Monotonicity and Applications Book PDF

Author : Andrew Eberhard,Nicolas Hadjisavvas,D.T. Luc
Publisher : Springer Science & Business Media
Page : 342 pages
File Size : 42,8 Mb
Release : 2006-06-22
Category : Business & Economics
ISBN : 9780387236391

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Generalized Convexity, Generalized Monotonicity and Applications by Andrew Eberhard,Nicolas Hadjisavvas,D.T. Luc Pdf

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.

Generalized Convexity, Generalized Monotonicity: Recent Results

Jean-Pierre Crouzeix,Juan Enrique Martinez Legaz,Michel Volle
Generalized Convexity Generalized Monotonicity Recent Results Book PDF

Author : Jean-Pierre Crouzeix,Juan Enrique Martinez Legaz,Michel Volle
Publisher : Springer Science & Business Media
Page : 469 pages
File Size : 45,6 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461333418

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Generalized Convexity, Generalized Monotonicity: Recent Results by Jean-Pierre Crouzeix,Juan Enrique Martinez Legaz,Michel Volle Pdf

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

Andrew Eberhard,Nicolas Hadjisavvas,D.T. Luc
Generalized Convexity Generalized Monotonicity and Applications Book PDF

Author : Andrew Eberhard,Nicolas Hadjisavvas,D.T. Luc
Publisher : Springer
Page : 0 pages
File Size : 51,9 Mb
Release : 2004-11-19
Category : Business & Economics
ISBN : 0387236384

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Generalized Convexity, Generalized Monotonicity and Applications by Andrew Eberhard,Nicolas Hadjisavvas,D.T. Luc Pdf

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.

Generalized Convexity

Sandor Komlosi,Tamas Rapcsak,Siegfried Schaible
Generalized Convexity Book PDF

Author : Sandor Komlosi,Tamas Rapcsak,Siegfried Schaible
Publisher : Springer Science & Business Media
Page : 406 pages
File Size : 40,6 Mb
Release : 2012-12-06
Category : Business & Economics
ISBN : 9783642468025

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Generalized Convexity by Sandor Komlosi,Tamas Rapcsak,Siegfried Schaible Pdf

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.

Generalized Convexity and Generalized Monotonicity

Nicolas Hadjisavvas,Juan E. Martinez-Legaz,Jean-Paul Penot
Generalized Convexity and Generalized Monotonicity Book PDF

Author : Nicolas Hadjisavvas,Juan E. Martinez-Legaz,Jean-Paul Penot
Publisher : Springer Science & Business Media
Page : 422 pages
File Size : 49,7 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783642566455

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Generalized Convexity and Generalized Monotonicity by Nicolas Hadjisavvas,Juan E. Martinez-Legaz,Jean-Paul Penot Pdf

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, Generalized Monotonicity, Optimality Conditions, and Duality in Scaler and Vector Optimization

Alberto Cambini,Bal Kishan Dass,Laura Martein
Generalized Convexity Generalized Monotonicity Optimality Conditions and Duality in Scaler and Vector Optimization Book PDF

Author : Alberto Cambini,Bal Kishan Dass,Laura Martein
Publisher : Unknown
Page : 416 pages
File Size : 43,7 Mb
Release : 2003
Category : Convex functions
ISBN : UOM:39015061544394

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Generalized Convexity, Generalized Monotonicity, Optimality Conditions, and Duality in Scaler and Vector Optimization by Alberto Cambini,Bal Kishan Dass,Laura Martein Pdf

The aim of this volume is to strengthen the interest in generalized convexity, generalized monotonicity and related areas and to stimulate new research in these fields by update survey (or recent results) of known experts covering many important topics such as some new theoretical aspects of generalized convexity and generalized invexity, some applications of generalized monotonicity and pseudomonotonicity to equilibrium problems and to economic and financial problems, some applications of abstract convexity, some applications of discrete convex analysis to cooperative game theory, fractional programming, optimality conditions in vector optimization (smooth and non-smooth), semi-infinite optimization and a new method for solving multiobjective problems.

Generalized Convexity and Optimization

Alberto Cambini,Laura Martein
Generalized Convexity and Optimization Book PDF

Author : Alberto Cambini,Laura Martein
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 47,6 Mb
Release : 2008-10-14
Category : Mathematics
ISBN : 9783540708766

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Generalized Convexity and Optimization by Alberto Cambini,Laura Martein Pdf

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.

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Generalized Convexity Nonsmooth Variational Inequalities and Nonsmooth Optimization Book PDF

Author : Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Publisher : CRC Press
Page : 294 pages
File Size : 46,9 Mb
Release : 2013-07-18
Category : Business & Economics
ISBN : 9781439868218

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Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization by Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta Pdf

Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction.The first part of the book focuses on generalized convexity and generalized

Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization

Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Generalized Convexity Nonsmooth Variational Inequalities and Nonsmooth Optimization Book PDF

Author : Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta
Publisher : CRC Press
Page : 298 pages
File Size : 43,6 Mb
Release : 2013-07-18
Category : Business & Economics
ISBN : 9781439868201

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Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization by Qamrul Hasan Ansari,C. S. Lalitha,Monika Mehta Pdf

Until now, no book addressed convexity, monotonicity, and variational inequalities together. Generalized Convexity, Nonsmooth Variational Inequalities, and Nonsmooth Optimization covers all three topics, including new variational inequality problems defined by a bifunction. The first part of the book focuses on generalized convexity and generalized monotonicity. The authors investigate convexity and generalized convexity for both the differentiable and nondifferentiable case. For the nondifferentiable case, they introduce the concepts in terms of a bifunction and the Clarke subdifferential. The second part offers insight into variational inequalities and optimization problems in smooth as well as nonsmooth settings. The book discusses existence and uniqueness criteria for a variational inequality, the gap function associated with it, and numerical methods to solve it. It also examines characterizations of a solution set of an optimization problem and explores variational inequalities defined by a bifunction and set-valued version given in terms of the Clarke subdifferential. Integrating results on convexity, monotonicity, and variational inequalities into one unified source, this book deepens your understanding of various classes of problems, such as systems of nonlinear equations, optimization problems, complementarity problems, and fixed-point problems. The book shows how variational inequality theory not only serves as a tool for formulating a variety of equilibrium problems, but also provides algorithms for computational purposes.

Generalized Convexity and Related Topics

Igor V. Konnov,Dinh The Luc,Alexander M. Rubinov
Generalized Convexity and Related Topics Book PDF

Author : Igor V. Konnov,Dinh The Luc,Alexander M. Rubinov
Publisher : Springer Science & Business Media
Page : 465 pages
File Size : 48,9 Mb
Release : 2006-11-22
Category : Business & Economics
ISBN : 9783540370079

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Generalized Convexity and Related Topics by Igor V. Konnov,Dinh The Luc,Alexander M. Rubinov Pdf

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.

Generalized Concavity

Mordecai Avriel,Walter E. Diewert,Siegfried Schaible,Israel Zang
Generalized Concavity Book PDF

Author : Mordecai Avriel,Walter E. Diewert,Siegfried Schaible,Israel Zang
Publisher : SIAM
Page : 342 pages
File Size : 41,9 Mb
Release : 2010-11-25
Category : Mathematics
ISBN : 9780898718966

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Generalized Concavity by Mordecai Avriel,Walter E. Diewert,Siegfried Schaible,Israel Zang Pdf

Originally published: New York: Plenum Press, 1988.

Convex Analysis and Monotone Operator Theory in Hilbert Spaces

Heinz H. Bauschke,Patrick L. Combettes
Convex Analysis and Monotone Operator Theory in Hilbert Spaces Book PDF

Author : Heinz H. Bauschke,Patrick L. Combettes
Publisher : Springer
Page : 624 pages
File Size : 42,8 Mb
Release : 2017-02-28
Category : Mathematics
ISBN : 9783319483115

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Convex Analysis and Monotone Operator Theory in Hilbert Spaces by Heinz H. Bauschke,Patrick L. Combettes Pdf

This reference text, now in its second edition, offers a modern unifying presentation of three basic areas of nonlinear analysis: convex analysis, monotone operator theory, and the fixed point theory of nonexpansive operators. Taking a unique comprehensive approach, the theory is developed from the ground up, with the rich connections and interactions between the areas as the central focus, and it is illustrated by a large number of examples. The Hilbert space setting of the material offers a wide range of applications while avoiding the technical difficulties of general Banach spaces. The authors have also drawn upon recent advances and modern tools to simplify the proofs of key results making the book more accessible to a broader range of scholars and users. Combining a strong emphasis on applications with exceptionally lucid writing and an abundance of exercises, this text is of great value to a large audience including pure and applied mathematicians as well as researchers in engineering, data science, machine learning, physics, decision sciences, economics, and inverse problems. The second edition of Convex Analysis and Monotone Operator Theory in Hilbert Spaces greatly expands on the first edition, containing over 140 pages of new material, over 270 new results, and more than 100 new exercises. It features a new chapter on proximity operators including two sections on proximity operators of matrix functions, in addition to several new sections distributed throughout the original chapters. Many existing results have been improved, and the list of references has been updated. Heinz H. Bauschke is a Full Professor of Mathematics at the Kelowna campus of the University of British Columbia, Canada. Patrick L. Combettes, IEEE Fellow, was on the faculty of the City University of New York and of Université Pierre et Marie Curie – Paris 6 before joining North Carolina State University as a Distinguished Professor of Mathematics in 2016.

Optimization of Complex Systems: Theory, Models, Algorithms and Applications

Hoai An Le Thi,Hoai Minh Le,Tao Pham Dinh
Optimization of Complex Systems Theory Models Algorithms and Applications Book PDF

Author : Hoai An Le Thi,Hoai Minh Le,Tao Pham Dinh
Publisher : Springer
Page : 1164 pages
File Size : 42,5 Mb
Release : 2019-06-15
Category : Technology & Engineering
ISBN : 9783030218034

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Optimization of Complex Systems: Theory, Models, Algorithms and Applications by Hoai An Le Thi,Hoai Minh Le,Tao Pham Dinh Pdf

This book contains 112 papers selected from about 250 submissions to the 6th World Congress on Global Optimization (WCGO 2019) which takes place on July 8–10, 2019 at University of Lorraine, Metz, France. The book covers both theoretical and algorithmic aspects of Nonconvex Optimization, as well as its applications to modeling and solving decision problems in various domains. It is composed of 10 parts, each of them deals with either the theory and/or methods in a branch of optimization such as Continuous optimization, DC Programming and DCA, Discrete optimization & Network optimization, Multiobjective programming, Optimization under uncertainty, or models and optimization methods in a specific application area including Data science, Economics & Finance, Energy & Water management, Engineering systems, Transportation, Logistics, Resource allocation & Production management. The researchers and practitioners working in Nonconvex Optimization and several application areas can find here many inspiring ideas and useful tools & techniques for their works.

Convex Optimization

Stephen P. Boyd,Lieven Vandenberghe
Convex Optimization Book PDF

Author : Stephen P. Boyd,Lieven Vandenberghe
Publisher : Cambridge University Press
Page : 744 pages
File Size : 48,5 Mb
Release : 2004-03-08
Category : Business & Economics
ISBN : 0521833787

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Convex Optimization by Stephen P. Boyd,Lieven Vandenberghe Pdf

Convex optimization problems arise frequently in many different fields. This book provides a comprehensive introduction to the subject, and shows in detail how such problems can be solved numerically with great efficiency. The book begins with the basic elements of convex sets and functions, and then describes various classes of convex optimization problems. Duality and approximation techniques are then covered, as are statistical estimation techniques. Various geometrical problems are then presented, and there is detailed discussion of unconstrained and constrained minimization problems, and interior-point methods. The focus of the book is on recognizing convex optimization problems and then finding the most appropriate technique for solving them. It contains many worked examples and homework exercises and will appeal to students, researchers and practitioners in fields such as engineering, computer science, mathematics, statistics, finance and economics.