Generalized Convexity and Related Topics

Generalized Convexity and Related Topics

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Overview

Generalized Convexity and Related Topics by Igor V. Konnov

In mathematics generalization is one of the main activities of researchers. It opens up new theoretical horizons and broadens the ?elds of applications. Intensive study of generalized convex objects began about three decades ago when the theory of convex analysis nearly reached its perfect stage of devel- ment with the pioneering contributions of Fenchel, Moreau, Rockafellar and others. The involvement of a number of scholars in the study of generalized convex functions and generalized monotone operators in recent years is due to the quest for more general techniques that are able to describe and treat models of the real world in which convexity and monotonicity are relaxed. Ideas and methods of generalized convexity are now within reach not only in mathematics, but also in economics, engineering, mechanics, ?nance and other applied sciences. This volume of referred papers, carefully selected from the contributions delivered at the 8th International Symposium on Generalized Convexity and Monotonicity (Varese, 4-8 July, 2005), o?ers a global picture of current trends of research in generalized convexity and generalized monotonicity. It begins withthreeinvitedlecturesbyKonnov,LevinandPardalosonnumericalvar- tionalanalysis,mathematicaleconomicsandinvexity,respectively.Thencome twenty four full length papers on new achievements in both the theory of the ?eld and its applications. The diapason of the topics tackled in these cont- butions is very large. It encompasses, in particular, variational inequalities, equilibrium problems, game theory, optimization, control, numerical me- ods in solving multiobjective optimization problems, consumer preferences, discrete convexity and many others.

Product Details

ISBN-13: 9783540370062
Publisher: Springer Berlin Heidelberg
Publication date: 11/16/2006
Series: Lecture Notes in Economics and Mathematical Systems , #583
Edition description: 2006
Pages: 472
Product dimensions: 6.10(w) x 9.25(h) x 0.04(d)

Table of Contents

Invited Papers.- Combined Relaxation Methods for Generalized Monotone Variational Inequalities.- Abstract Convexity and the Monge-Kantorovich Duality.- Optimality Conditions and Duality for Multiobjective Programming Involving (C, ?, ?, d) type-I Functions.- Contributed Papers.- Partitionable Variational Inequalities with Multi-valued Mappings.- Almost Convex Functions: Conjugacy and Duality.- Pseudomonotonicity of a Linear Map on the Interior of the Positive Orthant.- An Approach to Discrete Convexity and Its Use in an Optimal Fleet Mix Problem.- A Unifying Approach to Solve a Class of Parametrically-Convexifiable Problems.- Mathematical Programming with (?, ?)-invexity.- Some Classes of Pseudoconvex Fractional Functions via the Charnes-Cooper Transformation.- Equilibrium Problems Via the Palais-Smale Condition.- Points of Efficiency in Vector Optimization with Increasing-along-rays Property and Minty Variational Inequalities.- Higher Order Properly Efficient Points in Vector Optimization.- Higher-order Pseudoconvex Functions.- Sufficient Optimality Conditions and Duality in Nonsmooth Multiobjective Optimization Problems under Generalized Convexity.- Optimality Conditions for Tanaka’s Approximate Solutions in Vector Optimization.- On the Work of W. Oettli in Generalized Convexity and Nonconvex Optimization — a Review and Some Perspectives.- Local and Global Consumer Preferences.- Optimality Conditions for Convex Vector Functions by Mollified Derivatives.- On Arcwise Connected Convex Multifunctions.- A Sequential Method for a Class of Bicriteria Problems.- Decomposition of the Measure in the Integral Representation of Piecewise Convex Curves.- Rambling Through Local Versions of Generalized Convex Functions and Generalized Monotone Operators.- Monotonicity and Dualities.- On Variational-like Inequalities with Generalized Monotone Mappings.- Almost Pure Nash Equilibria in Convex Noncooperative Games.- A Spectral Approach to Solve Box-constrained Multi-objective Optimization Problems.

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