An improved infeasible SSLE method for constrained optimization without strict complementarity

In this paper, using “working set” technique for determining the active set, a new SSLE-Type algorithm with arbitrary initial point for constrained optimization is presented. At each iteration, we first introduce a new working set based on a multiplier function, then an improved direction is obtained by three systems of linear equations with the same coefficient matrix and possess small scale, and to avoid the Maratos effect, another correction direction is yielded by a simple explicit formula. Under some mild conditions, the algorithm is proved to be globally and strongly convergent, and the superlinear or even quadratic convergence can be obtained without the strict complementarity. Finally, some interesting numerical results are reported.