A trust region and affine scaling interior point method for nonconvex minimization with linear inequality constraints

A trust region and affine scaling interior point method (TRAM) is proposed for a general nonlinear minimization with linear inequality constraints [8] . In the proposed approach, a Newton step is derived from the complementari ty conditions. Based on this Newton step, a trust region subproblem is form ed, and the original objective function is monotonically decreased. Explici t sufficient decrease conditions are proposed for satisfying the first orde r and second order necessary conditions. The objective of this paper is to establish global and local convergence pr operties of the proposed trust region and affine scaling interior point met hod. It is shown that the proposed explicit decrease conditions are suffici ent for satisfy complementarity, dual feasibility and second order necessar y conditions respectively. It is also established that a trust region solut ion is asymptotically in the interior of the proposed trust region subprobl em and a properly damped trust region step can achieve quadratic convergenc e.