Rapport de recherche n° 2000-01

Auteur : Paul Armand, Jean-Charles Gilbert, Sophie Jan-Jégou

Titre : A Feasible BFGS Interior Point Algorithm for Solving Strongly Convex Minimization Problems

Nbre de pages : 31

Documents : Article (PDF), Article (PS)

Abstract: We propose a BFGS primal-dual interior point method for minimizing a convex function on a convex set defined by equality and inequality constraints. The algorithm generates feasible iterates and consists in computing approximate solutions of the optimality conditions perturbed by a sequence of positive parameters m converging to zero. We prove that it converges q-superlinearly for each fixed m. We also show that it is globally convergent to the analytic center of the primal-dual optimal set, when m tends to 0 and strict complementarity holds.  

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