An Affine Scaling Interior Point Filter Line-Search Algorithm for Linear Inequality Constrained Minimization

We propose and analyze a new affine scaling interior point method in association with line-search filter technique for solving the linear inequality constrained optimization. We extend an existing filter of Wchter and Biegler [9] for nonlinear equality constrained problems to linear inequality constraint problems. The two main ingredients of the method are a filter-line-search algorithm which is used to determine step size and an affine-scaling interior point Newton method which is used to generate a search direction. The global convergence of the proposed algorithm is established under some reasonable conditions. Further, the method is shown to be locally Q-superlinearly convergent under the strong second order sufficiency condition. Numerical tests are presented that confirm the robustness and efficiency of the approach.