A SSLE-Type Algorithm Combining The Method Of Strongly Sub-Feasible Direction With Working Set For Constrained Optimization

Sequential systems of linear equations (SSLE) algorithms are important algorithms for solving nonlinearly constrained optimization. In the recent years, SSLE algorithms have been widely studied since they generally have good convergence properties, and do not require solving any QP subproblems at each iteration. However, most of the SSLE algorithms usually require an initial feasible point, which is not easy to be obtained in generally, especially for large scale problems. To overcome this shortcoming, some SSLE algorithms with arbitrary initial points attract many experts and have been further studied.In this paper, by means of a new efficient identification technique of active constraints and the method of strongly sub-feasible direction, we propose a new sequential systems of linear equations (SSLE) algorithm for constrained optimization, in which the initial point is arbitrary. At each iteration, we first yield the working set by a pivoting operation and the gradient projection technique; then, three or four reduced linear equations with the same coefficients are solved to obtain the search direction. After a finite number of iterations, the algorithm can produced a feasible iteration point and it becomes the method of feasible directions. In particular, a new working set is adopted in our algorithm to further reduce the computational cost, and it also keeps all the advantages of working set. Under some mild conditions, the proposed algorithm is proved to be globally, strongly and superlinearly convergent. Finally, some preliminary numerical experiments are reported to show that the proposed algorithm is effective.