INTERIOR POINT METHOD FOR NONLINEAR OPTIMIZATION

Abstract

The line search methods are effective tool to solve nonlinear optimization problems. A variant line search method namely interior point estimation method has been effectively efficient to solve nonlinear constrained optimization problems. In this report we will present an interior point estimation method that solves perturbed Karush Kuhn Tucker conditions in a primal-dual optimization problem. At each iteration of the interior point estimation method, the algorithmic process computes the direction in which to be proceeded, and then calculates the suitable step length along the search direction. In order to compute the search direction, interior point estimation method utilizes Newton method and a merit function to decide a step length that balances the conflicting situation of reducing the objective function with satisfying the constraints. The proposed computation method is investigated on some test problems and real world problems. Further numerical comparison with existing methods shows that the computation process is efficient.