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

### Paul Armand, J. Charles Gilbert, Sophie Jan-J\'egou

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~$\mu$ converging to zero. We prove that it converges $q$-superlinearly for each fixed $\mu$ and that it is globally convergent when $\mu\to0$.

Research Report 3500, INRIA, France

Contact: Jean-Charles.Gilbert@inria.fr