INTERIOR POINT PROJECTED REDUCED HESSIAN METHOD WITH TRUST REGION STRATEGY FOR NONLINEAR CONSTRAINED OPTIMIZATION

§1　IntroductionIn this paper we analyze an interior point scaling projected reduced Hessian methodwith trust region strategy for solving the nonlinear equality constrained optimizationproblem with nonnegative constraints on variables:min　f(x)s.t.　c(x) =0 (1.1)x≥0where f∶Rn→R is the smooth nonlinear function,notnecessarily convex and c(x)∶Rn→Rm(m≤n) is the vector nonlinear function.There are quite a few articles proposing localsequential quadratic programming reduced Hessian methods…

INTERIOR POINT PROJECTED REDUCED HESSIAN METHOD WITH TRUST REGION STRATEGY FOR NONLINEAR CONSTRAINED OPTIMIZATION

A interior point scaling projected reduced Hessian method with combination of nonmonotonic backtracking technique and trust region strategy for nonlinear equality constrained optimization with nonegative constraint on variables is proposed.In order to deal with large problems,a pair of trust region subproblems in horizontal and vertical subspaces is used to replace the general full trust region subproblem.The horizontal trust region subproblem in the algorithm is only a general trust region subproblem while the vertical trust region subproblem is defined by a parameter size of the vertical direction subject only to an ellipsoidal constraint.Both trust region strategy and line search technique at each iteration switch to obtaining a backtracking step generated by the two trust region subproblems.By adopting the l 1 penalty function as the merit function, the global convergence and fast local convergence rate of the proposed algorithm are established under some reasonable conditions.A nonmonotonic criterion and the second order correction step are used to overcome Maratos effect and speed up the convergence progress in some ill conditioned cases.