Superlinear convergence of affine scaling interior point newton method for linear inequality constrained minimization without strict complementarity

Abstract

In this paper we extend and improve the classical affine scaling interior-point Newton method for solving nonlinear optimization subject to linear inequality constraints in the absence of the strict complementarity assumption. Introducing a computationally efficient technique and employing an identification function for the definition of the new affine scaling matrix, we propose and analyze a new affine scaling interior-point Newton method which improves the Coleman and Li affine scaling matrix in [2] for solving the linear inequality constrained optimization. Local superlinear and quadratical convergence of the proposed algorithm is established under the strong second order sufficiency condition without assuming strict complementarity of the solution.