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Generalized Convexity, Generalized Monotonicity: Recent Results

2013-12-01 Mathematics
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Release : 2013-12-01
Genre : Mathematics
Kind : eBook
Book Rating : 415/5 ( reviews)

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Book Synopsis Generalized Convexity, Generalized Monotonicity: Recent Results by : Jean-Pierre Crouzeix

Download or read book Generalized Convexity, Generalized Monotonicity: Recent Results written by Jean-Pierre Crouzeix. This book was released on 2013-12-01. Available in PDF, EPUB and Kindle. Book excerpt: 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

2006-06-22 Business & Economics
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Release : 2006-06-22
Genre : Business & Economics
Kind : eBook
Book Rating : 392/5 ( reviews)

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Book Synopsis Generalized Convexity, Generalized Monotonicity and Applications by : Andrew Eberhard

Download or read book Generalized Convexity, Generalized Monotonicity and Applications written by Andrew Eberhard. This book was released on 2006-06-22. Available in PDF, EPUB and Kindle. Book excerpt: 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

2006-01-16 Mathematics
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Release : 2006-01-16
Genre : Mathematics
Kind : eBook
Book Rating : 938/5 ( reviews)

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Book Synopsis Handbook of Generalized Convexity and Generalized Monotonicity by : Nicolas Hadjisavvas

Download or read book Handbook of Generalized Convexity and Generalized Monotonicity written by Nicolas Hadjisavvas. This book was released on 2006-01-16. Available in PDF, EPUB and Kindle. Book excerpt: 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

2004-11-19 Business & Economics
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Release : 2004-11-19
Genre : Business & Economics
Kind : eBook
Book Rating : 384/5 ( reviews)

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Book Synopsis Generalized Convexity, Generalized Monotonicity and Applications by : Andrew Eberhard

Download or read book Generalized Convexity, Generalized Monotonicity and Applications written by Andrew Eberhard. This book was released on 2004-11-19. Available in PDF, EPUB and Kindle. Book excerpt: 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 and Optimization

2008-10-14 Mathematics
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Release : 2008-10-14
Genre : Mathematics
Kind : eBook
Book Rating : 766/5 ( reviews)

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Book Synopsis Generalized Convexity and Optimization by : Alberto Cambini

Download or read book Generalized Convexity and Optimization written by Alberto Cambini. This book was released on 2008-10-14. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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