A Global Convergence Analysis of an Algorithm for Large-Scale Nonlinear Optimization Problems

Abstract

In this paper we give a global convergence analysis of a basic version of an SQP algorithm described in [P. T. Boggs, A. J. Kearsley, and J. W. Tolle, SIAM J. Optim., 9 (1999), pp. 755--778] for the solution of large-scale nonlinear inequality-constrained optimization problems. Several procedures and options have been added to the basic algorithm to improve the practical performance; some of these are also analyzed. The important features of the algorithm include the use of a constrained merit function to assess the progress of the iterates and a sequence of approximate merit functions that are less expensive to evaluate. It also employs an interior point quadratic programming solver that can be terminated early to produce a truncated step.