A Trust Region and Affine Scaling Method for Nonlinearly Constrained Minimization

Abstract. A nonlinearly constrained minimization problem can be solved by the exact penalty approach involving nondifferentiable functions and max 0 . In this paper, a trust region approach based on a 2-norm subproblem is proposed for solving a nonlinear 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. The global convergence analysis of the method is presented in [14].