An Improved Sequential Quadratic Programming Algorithm for Solving General Nonlinear Programming Problems

TL;DR

This paper introduces an enhanced SQP algorithm for nonlinear programming that combines quadratic programming and linear system solutions, achieving global superlinear convergence without strict complementarity.

Contribution

A novel SQP algorithm that integrates SLE solutions and higher-order corrections, improving convergence and efficiency for general nonlinear programming problems.

Findings

The algorithm demonstrates superlinear convergence under certain conditions.

Numerical results show improved efficiency over existing methods.

The method effectively handles problems without strict complementarity.

Abstract

In this paper, a class of general nonlinear programming problems with inequality and equality constraints is discussed. Firstly, the original problem is transformed into an associated simpler equivalent problem with only inequality constraints. Then, inspired by the ideals of sequential quadratic programming (SQP) method and the method of system of linear equations (SLE), a new type of SQP algorithm for solving the original problem is proposed. At each iteration, the search direction is generated by the combination of two directions, which are obtained by solving an always feasible quadratic programming (QP) subproblem and a SLE, respectively. Moreover, in order to overcome the Maratos effect, the higher-order correction direction is obtained by solving another SLE. The two SLEs have the same coefficient matrices, and we only need to solve the one of them after a finite number of iterations. By a new line search technique, the proposed algorithm possesses global and superlinear convergence under some suitable assumptions without the strict complementarity. Finally, some comparative numerical results are reported to show that the proposed algorithm is effective and promising.