A Feasible BFGS Interior Point Algorithm for Solving Convex Minimization Problems

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 μ converging to zero. We prove that it converges q-superlinearly for each fixed μ. We also show that it is globally convergent to the analytic center of the primal-dual optimal set when μ tends to 0 and strict complementarity holds.