Hierarchical solution concept for static and multistage decision problems with two objectives
Homogeneous functions and conjugacy.
How much do approximate derivatives hurt filter methods?
In this paper, we examine the influence of approximate first and/or second derivatives on the filter-trust-region algorithm designed for solving unconstrained nonlinear optimization problems and proposed by Gould, Sainvitu and Toint in [12]. Numerical experiments carried out on small-scaled unconstrained problems from the CUTEr collection describe the effect of the use of approximate derivatives on the robustness and the efficiency of the filter-trust-region method.
Implémentation des méthodes d'optimisation : test d'arrêt optimal, contrôle et précision de la solution
Implementation of penalty function methods in LISP
Improved local convergence analysis of inexact Newton-like methods under the majorant condition
We present a local convergence analysis of inexact Newton-like methods for solving nonlinear equations. Using more precise majorant conditions than in earlier studies, we provide: a larger radius of convergence; tighter error estimates on the distances involved; and a clearer relationship between the majorant function and the associated least squares problem. Moreover, these advantages are obtained under the same computational cost.
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...
Integer Programming Formulation of the Bilevel Knapsack Problem
The Bilevel Knapsack Problem (BKP) is a hierarchical optimization problem in which the feasible set is determined by the set of optimal solutions of parametric Knapsack Problem. In this paper, we propose two stages exact method for solving the BKP. In the first stage, a dynamic programming algorithm is used to compute the set of reactions of the follower. The second stage consists in solving an integer program reformulation of BKP. We show that the...
Invariants of pairs of compact convex sets.
Iterative Optimierungsverfahren, die unter schwachen Voraussetzungen konvergieren.
Kolmogorov problem in and extremal Zolotarev ω-splines [Book]
Kuhn-Tucker-Theorie für Funktionen mit Richtungsableitungen
La différentiation automatique et son utilisation en optimisation
In this work, we present an introduction to automatic differentiation, its use in optimization software, and some new potential usages. We focus on the potential of this technique in optimization. We do not dive deeply in the intricacies of automatic differentiation, but put forward its key ideas. We sketch a survey, as of today, of automatic differentiation software, but warn the reader that the situation with respect to software evolves rapidly. In the last part of the paper, we present some...
La programación geométrica en la economía de las producciones ganaderas.
Se modeliza el problema no lineal de producción de carne de vacuno por Programación Geométrica Signomial. Los datos técnicos utilizados se han extraído del trabajo de Epplin y Heady (1984). Se aplican transformaciones inversas y métodos de condensación al problema signomial para simplificar el modelo teórico. Finalmente, se calcula la composición de la ración óptima, bajo distintas consideraciones y se comentan los resultados obtenidos, que confirman y completan otros experimentales ya existentes...
La programmation mathématique multicritère et la gestion des ressources en eau
Lagrange principle and necessary conditions
Large-scale nonlinear programming algorithm using projection methods
A method for solving large convex optimization problems is presented. Such problems usually contain a big linear part and only a small or medium nonlinear part. The parts are tackled using two specialized (and thus efficient) external solvers: purely nonlinear and large-scale linear with a quadratic goal function. The decomposition uses an alteration of projection methods. The construction of the method is based on the zigzagging phenomenon and yields a non-asymptotic convergence, not dependent...
Le point sur quelques méthodes directes de recherche de l'extremum d'une fonction monodimensionnelle unimmodale
Lineare Optimierung in halbgeordneten Vektorräumen.
Local Convergence Analysis for Partitioned Quasi-Newton Updates.