Fenchel Type Duality Theorems in Finite Dimensional Ordered Vector Spaces.
First Order Characterizations of Pseudoconvex Functions
First order characterizations of pseudoconvex functions are investigated in terms of generalized directional derivatives. A connection with the invexity is analysed. Well-known first order characterizations of the solution sets of pseudolinear programs are generalized to the case of pseudoconvex programs. The concepts of pseudoconvexity and invexity do not depend on a single definition of the generalized directional derivative.
Flots entiers et multiflots fractionnaires couplés par une contrainte de capacité
Nous modélisons ici plusieurs problèmes de Transport et de Gestion de Flux à l’aide d’un flot entier et d’un multiflot fractionnaire couplés par une contrainte de capacité. Pour le problème ainsi obtenu, nous proposons différents schémas de résolution par relaxation et décomposition, qui induisent la recherche d’un flot auxiliaire dont la partie entière supérieure doit minimiser un certain coût, et qui requièrent la mise en œuvre d’un processus d’agrégation. Nous en déduisons diverses heuristiques...
Flots entiers et multiflots fractionnaires couplés par une contrainte de capacité
Nous modélisons ici plusieurs problèmes de Transport et de Gestion de Flux à l'aide d'un flot entier et d'un multiflot fractionnaire couplés par une contrainte de capacité. Pour le problème ainsi obtenu, nous proposons différents schémas de résolution par relaxation et décomposition, qui induisent la recherche d'un flot auxiliaire dont la partie entière supérieure doit minimiser un certain coût, et qui requièrent la mise en œuvre d'un processus d'agrégation. Nous en déduisons diverses heuristiques...
Fritz John's type conditions and associated duality forms in convex non differentiable vector-optimization
From Eckart and Young approximation to Moreau envelopes and vice versa
In matricial analysis, the theorem of Eckart and Young provides a best approximation of an arbitrary matrix by a matrix of rank at most r. In variational analysis or optimization, the Moreau envelopes are appropriate ways of approximating or regularizing the rank function. We prove here that we can go forwards and backwards between the two procedures, thereby showing that they carry essentially the same information.
Gain-loss pricing under ambiguity of measure
Motivated by the observation that the gain-loss criterion, while offering economically meaningful prices of contingent claims, is sensitive to the reference measure governing the underlying stock price process (a situation referred to as ambiguity of measure), we propose a gain-loss pricing model robust to shifts in the reference measure. Using a dual representation property of polyhedral risk measures we obtain a one-step, gain-loss criterion based theorem of asset pricing under ambiguity of...
General algorithm and sensitivity analysis for variational inequalities.
Generalized convexity and optimization problems
Generic well-posedness in minimization problems.
Graph-convex mappings and -convex functions.
Guaranteed and computable bounds of the limit load for variational problems with linear growth energy functionals
The paper is concerned with guaranteed and computable bounds of the limit (or safety) load, which is one of the most important quantitative characteristics of mathematical models associated with linear growth functionals. We suggest a new method for getting such bounds and illustrate its performance. First, the main ideas are demonstrated with the paradigm of a simple variational problem with a linear growth functional defined on a set of scalar valued functions. Then, the method is extended to...
Harmonic sum and duality.
Hybrid iterative methods for convex feasibility problems and fixed point problems of relatively nonexpansive mappings in Banach spaces.
Imperfect Conjugate Gradient Algorithms for Extended Quadratic Functions.
Implicit constitutive solution scheme for Mohr-Coulomb plasticity
This contribution summarizes an implicit constitutive solution scheme of the elastoplastic problem containing the Mohr-Coulomb yield criterion, a nonassociative flow rule, and a nonlinear isotropic hardening. The presented scheme builds upon the subdifferential formulation of the flow rule leading to several improvements. Mainly, it is possible to detect a position of the unknown stress tensor on the Mohr-Coulomb pyramid without blind guesswork. Further, a simplified construction of the consistent...
Impulse noise removal based on new hybrid conjugate gradient approach
Image denoising is a fundamental problem in image processing operations. In this paper, we present a two-phase scheme for the impulse noise removal. In the first phase, noise candidates are identified by the adaptive median filter (AMF) for salt-and-pepper noise. In the second phase, a new hybrid conjugate gradient method is used to minimize an edge-preserving regularization functional. The second phase of our algorithm inherits advantages of both Dai-Yuan (DY) and Hager-Zhang (HZ) conjugate gradient...
Inexact trust region method for large sparse nonlinear least squares
Interactive Method for Solving Multi-Objective Convex Programs
Introduction to the volume