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.