Sequential systems of linear equations method for general constrained optimization without strict complementarity

Abstract

In this paper, based on an l 1 - l ∞ hybrid exact penalty function, we proposed an infeasible SSLE method for general constrained optimization. An automatic adjustment rule is incorporated in the algorithm for the choice of the penalty parameter, which ensures that the penalty parameter be updated only finitely many times. We also extend the Facchinei–Fischer–Kanzow active-set identification technique to general constrained optimization and a corresponding identification function is given. At each iteration, only two or three reduced linear equations with the same coefficients are solved to obtain the search direction. Under the linear independence condition, the sequence generated by the new algorithm globally converges to a KKT point. In particular, the convergence rate is proved to be one-step superlinear without assuming the strict complementarity and under a condition weaker than the strong second-order sufficiency condition. Some preliminary numerical results indicate that the new algorithm is quite promising.