Unconstrained reformulation of sequential quadratic programming for solving optimization problems with linear equality constraints

Abstract

In this paper, we propose an alternative approach to Sequential Quadratic Programming (SQP) for solving optimization problems with linear equality constraints. The concept of a regularized gap function is employed to reformulate the constrained problem into an unconstrained one. The proposed algorithm incorporates a positive definite Hessian modification along with a backtracking line search to promote global convergence. Its effectiveness is demonstrated through several numerical experiments and geometric illustrations. Furthermore, applications of the proposed method are explored in optimal allocation, analytic center computation, and network flow problems.