This volume contains a collection of refereed articles on generalized convexity and generalized monotonicity. The first part of the book contains invited papers by leading experts (J.M. Borwein, R.E. Burkard, B.S. Mordukhovich and H. Tuy) with applications of (generalized) convexity to such diverse fields as algebraic dynamics of the Gamma function values, discrete optimization, Lipschitzian stability of parametric constraint systems, and monotonicity of functions. The second part contains contributions presenting the latest developments in generalized convexity and generalized monotonicity: its connections with discrete and with continuous optimization, multiobjective optimization, fractional programming, nonsmooth Aanalysis, variational inequalities, and its applications to concrete problems such as finding equilibrium prices in mathematical economics, or hydrothermal scheduling.
Audience
This volume is suitable for faculty, graduate students, and researchers in mathematical programming, operations research, convex analysis, nonsmooth analysis, game theory and mathematical economics.
Author(s): J. M. Borwein, K. Karamanos (auth.), Andrew Eberhard, Nicolas Hadjisavvas, Dinh The Luc (eds.)
Series: Nonconvex Optimization and Its Applications 77
Edition: 1
Publisher: Springer US
Year: 2005
Language: English
Pages: 350
Tags: Operations Research, Mathematical Programming; Optimization; Calculus of Variations and Optimal Control; Optimization; Game Theory, Economics, Social and Behav. Sciences
Front Matter....Pages 1-1
Algebraic Dynamics of Certain Gamma Function Values....Pages 3-21
(Generalized) Convexity and Discrete Optimization....Pages 23-37
Lipschitzian Stability of Parametric Constraint Systems in Infinite Dimensions....Pages 39-59
Monotonicity in the Framework of Generalized Convexity....Pages 61-85
Front Matter....Pages 87-87
On the Contraction and Nonexpansiveness Properties of the Marginal Mappings in Generalized Variational Inequalities Involving Co-Coercive Operators....Pages 89-111
A Projection-Type Algorithm for Pseudomonotone Nonlipschitzian Multivalued Variational Inequalities....Pages 113-129
Duality in Multiobjective Optimization Problems with Set Constraints....Pages 131-146
Duality in Fractional Programming Problems with Set Constraints....Pages 147-159
On the Pseudoconvexity of the Sum of Two Linear Fractional Functions....Pages 161-172
Bonnesen-Type Inequalities and Applications....Pages 173-181
Characterizing Invex and Related Properties....Pages 183-191
Minty Variational Inequality and Optimization: Scalar and Vector Case....Pages 193-211
Second Order Optimality Conditions for Nonsmooth Multiobjective Optimization Problems....Pages 213-228
Second Order Subdifferentials Constructed Using Integral Convolutions Smoothing....Pages 229-261
Applying Global Optimization to a Problem in Short-Term Hydrothermal Scheduling....Pages 263-285
ε -Optimality for Nonsmooth Programming on a Hilbert Space....Pages 287-297
Identification of Hidden Convex Minimization Problems....Pages 299-309
On Vector Quasi-Saddle Points of Set-Valued Maps....Pages 311-319
New Generalized Invexity for Duality in Multiobjective Programming Problems Involving N -Set Functions....Pages 321-339
Equilibrium Prices and Quasiconvex Duality....Pages 341-350
