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Generalized Convexity and Generalized Monotonicity: Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999(502 Lecture Notes in Economics and Mathematical Systems)

Generalized Convexity and Generalized Monotonicity: Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999(502 Lecture Notes in Economics and Mathematical Systems)

          
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About the Book

A famous saying (due toHerriot)definescultureas "what remainswhen everythingisforgotten ". One couldparaphrase thisdefinitionin statingthat generalizedconvexity iswhat remainswhen convexity has been dropped . Of course, oneexpectsthatsome convexityfeaturesremain.For functions, convexity ofepigraphs(what is above thegraph) is a simplebut strong assumption.It leads tobeautifulpropertiesand to a field initselfcalled convex analysis. In several models, convexity is not presentandintroducing genuine convexityassumptionswouldnotberealistic. A simple extensionof thenotionof convexity consists in requiringthatthe sublevel sets ofthe functionsare convex (recall thata sublevel set offunction a is theportionof thesourcespaceon which thefunctiontakesvalues below a certainlevel).Its first use is usuallyattributed to deFinetti,in 1949. This propertydefinesthe class ofquasiconvexfunctions, which is much larger thanthe class of convex functions: a non decreasingor nonincreasingone- variablefunctionis quasiconvex ,as well asanyone-variable functionwhich is nonincreasingon someinterval(-00,a] or(-00,a) and nondecreasingon its complement.Many otherclasses ofgeneralizedconvexfunctionshave been introduced ,often fortheneeds ofvariousapplications: algorithms ,economics, engineering ,management science,multicriteria optimization ,optimalcontrol, statistics . Thus,theyplay animportantrole in severalappliedsciences . A monotonemappingF from aHilbertspace to itself is a mappingfor which the angle between F(x) - F(y) and x- y isacutefor anyx, y. It is well-known thatthegradientof a differentiable convexfunctionis monotone.The class of monotonemappings(and theclass ofmultivaluedmonotoneoperators) has remarkableproperties.This class has beengeneralizedin various direc- tions,withapplicationsto partialdifferentialequations ,variationalinequal- ities,complementarity problemsand more generally, equilibriumproblems. The classes ofgeneralizedmonotonemappingsare more or lessrelatedto the classes ofgeneralizedfunctionsvia differentiation or subdifferentiation procedures.They are also link edvia severalothermeans.

Table of Contents:
Invited Papers.- Minimization of the Sum of Several Linear Fractional Functions.- Discrete Higher Order Convex Functions and their Applications.- Cuts and Semidefinite Relaxations for Nonconvex Quadratic Problems.- Contributed Papers.- The Steiner Ratio of L3p.- Normal Cones to Sublevel Sets: An Axiomatic Approach. Applications in Quasiconvexity and Pseudoconvexity.- Multiobjective Programming with ?-convex Functions.- Rufián-Lizana, Pascual Ruiz-Canales Vector Invex N-set Functions and Minmax Programming.- On the Supremum in Quadratic Fractional Programming.- First and Second Order Characterizations of a Class of Pseudoconcave Vector Functions.- New Invexity-Type Conditions in Constrained Optimization.- Stochastic s-(increasing) Convexity.- Fixed Point Theorems, Coincidence Theorems and Variational Inequalities.- Representation of a Polynomial Function as a Difference of Convex Polynomials, with an Application.- Proper Efficiency and Generalized Convexity in Nonsmooth Vector Optimization Problems.- Duality for Fractional Min-max Problems Involving Arcwise Connected and Generalized Arcwise Connected Functions.- Generalized Convexity for Unbounded Sets: The Enlarged Space.- A Note on Minty Variational Inequalities and Generalized Monotonicity.- On Vector Equilibrium and Vector Variational Inequality Problems.- Stochastic Orders Generated by Generalized Convex Functions.- Separation Theorems for Convex Sets and Convex Functions with Invariance Properties.- Convexity and Generalized Convexity Methods for the Study of Hamilton-Jacobi Equations.- Higher-order Monotone Functions and Probability Theory.- Convexity and Decomposability in Multivalued Analysis.- Scalar Characterization of Generalized Quasiconvex Functions.- Optimality and Wolfe Duality for MultiobjectiveProgramming Problems Involving?-set Functions.- Vector Stochastic Optimization Problems.- On Suprema of Abstract Convex and Quasi-convex Hulls.- Specific Numerical Methods for Solving Some Special Max-min Programming Problems Involving Generalized Convex Functions.


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Product Details
  • ISBN-13: 9783540418061
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Edition: 2001 ed.
  • Language: English
  • Returnable: Y
  • Spine Width: 22 mm
  • Weight: 593 gr
  • ISBN-10: 3540418067
  • Publisher Date: 10 Apr 2001
  • Binding: Paperback
  • Height: 235 mm
  • No of Pages: 410
  • Series Title: 502 Lecture Notes in Economics and Mathematical Systems
  • Sub Title: Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999
  • Width: 155 mm


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Generalized Convexity and Generalized Monotonicity: Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999(502 Lecture Notes in Economics and Mathematical Systems)
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Generalized Convexity and Generalized Monotonicity: Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999(502 Lecture Notes in Economics and Mathematical Systems)
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Generalized Convexity and Generalized Monotonicity: Proceedings of the 6th International Symposium on Generalized Convexity/Monotonicity, Samos, September 1999(502 Lecture Notes in Economics and Mathematical Systems)

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