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

We propose a BFGS primal-dual interior point method for minimizing a convex function on a convex set de ned 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 converging to zero. We prove that it converges qsuperlinearly for each xed . We also show that it is globally convergent to the analytic center of the primal-dual optimal set, when tends to 0 and strict complementarity holds.