A Trust Region and Affine Scaling Method for Nonlinearly Constrained Minimization

摘要

(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 the paper, 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 based on the approximations are suggested for obtaining a limit point satisfying complementarity, Kuhn-Tucker conditions, and second order necessary conditions. In global convergence analysis of the method is presented in [4].