The nonlinear programming method of Wilson, Han, and Powell with an augmented Lagrangian type line search function

Summary

The paper represents an outcome of an extensive comparative study of nonlinear optimization algorithms. This study indicates that quadratic approximation methods which are characterized by solving a sequence of quadratic subproblems recursively, belong to the most efficient and reliable nonlinear programming algorithms available at present. The purpose of this paper is to analyse the theoretical convergence properties and to investigate the numerical performance in more detail. In Part 1, the exactL ₁-penalty function of Han and Powell is replaced by a differentiable augmented Lagrange function for the line search computation to the able to prove the global convergence and to show that the steplength one is chosen in the neighbourhood of a solution. In Part 2, the quadratic subproblem is exchanged by a linear least squares problem to improve the efficiency, and to test the dependence of the performance from different solution methods for the quadratic or least squares subproblems.