Solving general nonlinear programming problems via trust region and conjugate gradient methods

摘要

In this paper, we develop an interior point trust region method for solving general nonlinear programming problems. The trust region subproblem is derived from reformulation of the KKT system as a simply constrained optimization problem and is solved by the truncated conjugate gradient method. To overcome the difficulty of repeated solving of the trust region subproblem, we use line search strategy to obtain next iterate when trust region trial step can not be accepted. The resulting algorithm generates sequence of points in the interior of feasible region automatically. A global convergence is established under suitable conditions.