Interior Point Method based Sequential Quadratic Programming Algorithm with Quadaratic Search for Nonlinear Optimization

Abstract

The field of constrained nonlinear programming (NLP) has been principally challenging to various gradient based optimization techniques. The Sequential quadratic programming algorithm (SQP) that uses active set strategy in solving quadratic programming (QP) subproblems proves to be efficient in locating the points of local optima. However, its efficient determination of the optimal active set heavily relies on the initial guess of the starting point. This remains a serious drawback to both primal and dual active set (AS) approaches especially for NLPs with several inequality constraints. Thus, we propose an SQP/IIPM algorithm that uses infeasible interior point method (IIPM) for solving QP subproblems. In this approach inequality constraints can be solved directly, alleviating the burden for choosing a feasible starting point necessary for efficient convergence to optimal active set. At every iteration k, we evaluate step length adaptively via a simple line search and/or a quadratic search algorithm depending on the reason for the termination of our IIPM QP solver. Our SQP/IIPM algorithm falls to line search whenever the termination of the IIPM QP solver satisfies the complementary slackness condition (i.e. duality measure). This means that neither the Primal nor the Dual feasibility conditions are satisfied during the termination of the IIPM QP solver. In addition, the algorithm can also switch to quadratic search whenever the line search algorithm exceeds its maximum iteration limit. Results of comparing SQP/IIPM with SQP reveal that, the proposed algorithm is efficient and promising.