A null-space primal-dual interior-point algorithm for nonlinear optimization with nice convergence properties

Abstract. We present a null-space primal-dual interior-point algorithm for solving nonlinear optimization problems with general inequality and equality constraints. The algorithm approximately solves a sequence of equality constrained barrier subproblems by computing a range-space step and a null-space step in every iteration. The 2 penalty function is taken as the merit function. Under very mild conditions on range-space steps and approximate Hessians, without assuming any regularity, it is proved that either every limit point of the iterate sequence is a Karush-Kuhn-Tucker point of the barrier subproblem and the penalty parameter remains bounded, or there exists a limit point that is either an infeasible stationary point of minimizing the 2 norm of violations of constraints of the original problem, or a Fritz-John point of the original problem. In addition, we analyze the local convergence properties of the algorithm, and prove that by suitably controlling the exactness of range-spac...

• Type: Journal
• Year: 2010
• Where: MP
• Authors: Xinwei Liu, Yaxiang Yuan
• Keywords: Barrier Subproblem, Equality Constraints, MP 2010, Range-space Steps