An Interior Point Algorithm for the General Nonlinear Programming Problem with Trust Region Globalization

摘要

This paper presents a sequential quadratic programming (SQP)-based interior point technique for solving the general nonlinear programming problem using trust region globalization and the Coleman-Li scaling. The SQP sub-problem is decomposed into a normal and a reduced tangential subproblem in the tradition of numerous works on equality constrained optimization, and strict feasibility is maintained with respect to the bounds. This is intended to be an extension of previous work by Coleman & Li and Vicente. Though no theoretical proofs of convergence are provided, some computational results are presented which indicate that this algorithm holds promise. The computational experiments have been geared towards improving the semi-local convergence of the algorithm; in particular high sensitivity of the speed of convergence with respect to the fraction of the trust region radius allowed for the normal step and with respect to the initial trust region radius are observed. The chief advantages of this algorithm over primal dual interior point algorithms are better handling of the 'sticking problem' and a reduction in the number of variables by elimination of the multipliers of bound constraints.