On Global Convergence of a Trust Region and Affine Scaling Method for Nonlinearly Constrained Minimization

Abstract

(The following contains mathematical formulae and symbols that may become distorted in ASCII text.) A nonlinearly constrained optimization problem can be solved by the exact penalty approach involving non differentiable functions (summation(i)of |ci(x)|) and (summation(i) of max(0,ci(x))). In [11], a trust region affine scaling approach based on a 2-norm subproblem is proposed for solving a nonlinear l 1 problem. The (quadratic) approximation and the trust region subproblem are defined using affine scaling techniques. Explicit sufficient decrease conditions are proposed to obtain a limitpoint satisfying complementarity, dual feasibility, and second order optimality. In this paper, we present the global convergence properties of this new approach.