On Some Convex Cones And Associated Monotone Functions PDF Download
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Author | : Donald P. Squier |
Publisher | : |
Total Pages | : 136 |
Release | : 1955 |
Genre | : Convex geometry |
ISBN | : |
Download On Some Convex Cones and Associated Monotone Functions Book in PDF, ePub and Kindle
Author | : Roy Martin Rakestraw |
Publisher | : |
Total Pages | : 136 |
Release | : 1969 |
Genre | : |
ISBN | : |
Download Convex Cones of N-monotone Functions Book in PDF, ePub and Kindle
Author | : R. Tyrrell Rockafellar |
Publisher | : American Mathematical Soc. |
Total Pages | : 78 |
Release | : 1967 |
Genre | : Convex domains |
ISBN | : 0821812777 |
Download Monotone Processes of Convex and Concave Type Book in PDF, ePub and Kindle
Author | : Nicolas Hadjisavvas |
Publisher | : Springer Science & Business Media |
Total Pages | : 684 |
Release | : 2006-01-16 |
Genre | : Mathematics |
ISBN | : 0387233938 |
Download Handbook of Generalized Convexity and Generalized Monotonicity Book in PDF, ePub and Kindle
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.
Author | : Jean-Pierre Crouzeix |
Publisher | : Springer Science & Business Media |
Total Pages | : 469 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461333415 |
Download Generalized Convexity, Generalized Monotonicity: Recent Results Book in PDF, ePub and Kindle
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.
Author | : Robert R. Phelps |
Publisher | : Springer Science & Business Media |
Total Pages | : 127 |
Release | : 1993-07-29 |
Genre | : Mathematics |
ISBN | : 3540567151 |
Download Convex Functions, Monotone Operators and Differentiability Book in PDF, ePub and Kindle
The improved and expanded second edition contains expositions of some major results which have been obtained in the years since the 1st edition. Theaffirmative answer by Preiss of the decades old question of whether a Banachspace with an equivalent Gateaux differentiable norm is a weak Asplund space. The startlingly simple proof by Simons of Rockafellar's fundamental maximal monotonicity theorem for subdifferentials of convex functions. The exciting new version of the useful Borwein-Preiss smooth variational principle due to Godefroy, Deville and Zizler. The material is accessible to students who have had a course in Functional Analysis; indeed, the first edition has been used in numerous graduate seminars. Starting with convex functions on the line, it leads to interconnected topics in convexity, differentiability and subdifferentiability of convex functions in Banach spaces, generic continuity of monotone operators, geometry of Banach spaces and the Radon-Nikodym property, convex analysis, variational principles and perturbed optimization. While much of this is classical, streamlined proofs found more recently are given in many instances. There are numerous exercises, many of which form an integral part of the exposition.
Author | : L. S. Arendarenko |
Publisher | : |
Total Pages | : 23 |
Release | : 2011 |
Genre | : |
ISBN | : |
Download Some new ineqaualities on cones of monotone functions Book in PDF, ePub and Kindle
Author | : Library of Congress. Science and Technology Division |
Publisher | : |
Total Pages | : 1196 |
Release | : 1961 |
Genre | : Military research |
ISBN | : |
Download Air Force Scientific Research Bibliography: 1950-56 Book in PDF, ePub and Kindle
Author | : Jonathan M. Borwein |
Publisher | : Cambridge University Press |
Total Pages | : 533 |
Release | : 2010-01-14 |
Genre | : Mathematics |
ISBN | : 1139811096 |
Download Convex Functions Book in PDF, ePub and Kindle
Like differentiability, convexity is a natural and powerful property of functions that plays a significant role in many areas of mathematics, both pure and applied. It ties together notions from topology, algebra, geometry and analysis, and is an important tool in optimization, mathematical programming and game theory. This book, which is the product of a collaboration of over 15 years, is unique in that it focuses on convex functions themselves, rather than on convex analysis. The authors explore the various classes and their characteristics and applications, treating convex functions in both Euclidean and Banach spaces. The book can either be read sequentially for a graduate course, or dipped into by researchers and practitioners. Each chapter contains a variety of specific examples, and over 600 exercises are included, ranging in difficulty from early graduate to research level.
Author | : Jein-Shan Chen |
Publisher | : Springer |
Total Pages | : 206 |
Release | : 2019-02-11 |
Genre | : Business & Economics |
ISBN | : 9811340773 |
Download SOC Functions and Their Applications Book in PDF, ePub and Kindle
This book covers all of the concepts required to tackle second-order cone programs (SOCPs), in order to provide the reader a complete picture of SOC functions and their applications. SOCPs have attracted considerable attention, due to their wide range of applications in engineering, data science, and finance. To deal with this special group of optimization problems involving second-order cones (SOCs), we most often need to employ the following crucial concepts: (i) spectral decomposition associated with SOCs, (ii) analysis of SOC functions, and (iii) SOC-convexity and -monotonicity. Moreover, we can roughly classify the related algorithms into two categories. One category includes traditional algorithms that do not use complementarity functions. Here, SOC-convexity and SOC-monotonicity play a key role. In contrast, complementarity functions are employed for the other category. In this context, complementarity functions are closely related to SOC functions; consequently, the analysis of SOC functions can help with these algorithms.