Abstract: In this paper, based on an active set identification technique, a new feasible sequential system of linear equations (SSLE) algorithm is proposed for nonlinear optimization problems with inequality constraints. At each iteration, only two or three systems of linear equations with a common coefficient matrix are solved to obtain the search direction. Under mild conditions, the suggested algorithm converges globally to a KKT point of the problem. Without assuming the strict complementarity, the convergence rate is proved to be superlinear under a condition weaker than the strong second-order sufficiency condition.

Key words: Sequential systems of linear equations method, Optimization, Global convergence, Superlinear convergence