The Linear Convergence of a Successive Linear Programming Algorithm

Abstract

We present a successive linear programming algorithm for solving constrained nonlinear optimization problems. The algorithm employs an Armijo procedure for updating a trust region radius. We prove the linear convergence of the method by relating the solutions of our subproblems to standard trust region and gradient projection subproblems and adapting an error bound analysis due to Luo and Tseng. Computational results are provided for polyhedrally constrained nonlinear programs.