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,