Interior methods provide an effective approach for the treatment of inequality constraints in nonlinearly constrained optimization. A new primal-dual interior method is proposed based on minimizing a sequence of shifted primal-dual penalty-barrier functions. Certain global convergence properties are established. In particular, it is shown that every limit point is either an infeasible stationary point, or an approximate KKT point, i.e., it satisfies reasonable stopping criteria for a local minimizer and is a KKT point under a weak constraint qualification. It is shown that under suitable assumptions, the method is equivalent to the conventional path-following interior method in the neighborhood of a solution.
Technical Report CCoM-18-1, UCSD Center for Computational Mathematics, UC San Diego, February 2018.