A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Journal Articles Mathematical Programming Year : 2002

A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach

Sophie Jan
Paul Armand

Abstract

This paper introduces and analyses a new algorithm for minimizing a convex function subject to a finite number of convex inequality constraints. It is assumed that the Lagrangian of the problem is strongly convex. The algorithm combines interior point methods for dealing with the inequality constraints and quasi-Newton techniques for accelerating the convergence. Feasibility of the iterates is progressively enforced thanks to shift variables and an exact penalty approach. Global and $q$-superlinear convergenc- e is obtained for a fixed penalty parameter; global convergence to the analytic center of the optimal set is ensured when the barrier parameter tends to zero, provided strict complementarity holds.
Fichier principal
Vignette du fichier
RR-4087.pdf (415.75 Ko) Télécharger le fichier

Dates and versions

inria-00072546 , version 1 (24-05-2006)

Licence

Attribution - NoDerivatives

Identifiers

Cite

Jean Charles Gilbert, Sophie Jan, Paul Armand. A BFGS-IP algorithm for solving strongly convex optimization problems with feasibility enforced by an exact penalty approach. Mathematical Programming, 2002, 92 (3), pp.393-424. ⟨10.1007/s101070100283⟩. ⟨inria-00072546⟩
128 View
212 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More