A Trust Region and Affine Scaling Interior Point Method for NonconvexMinimization with Linear Inequality Constraints

Abstract

A trust region and affine scaling interior point method (TRAM) is proposed for a general nonlinear minimization with linear inequality constraints in [8]. In the proposed approach, a Newton step is derived from the complementarity conditions. Based on this Newton step, a trust region subproblem is formed, and the original objective function is monotonically decreased. Explicit sufficient decrease conditions are proposed for satisfying complementarity, dual feasibility and second order optimality. The objective of this paper is to establish global and local convergence properties of the proposed trust region and affine scaling interior point method. It is shown that the proposed decrease conditions are sufficient for achieving complementarity, dual feasibility and second order optimality respectively. It is also established that a trust region solution is asymptotically in the interior of the proposed trust region subproblem and a damped trust region step can achieve quadratic convergence.