A superlinearly and quadratically convergent SQP type feasible method for constrained optimization

A new SQP type feasible method for inequality constrained optimization is presented, it is a combination of a master algorithm and an auxiliary algorithm which is taken only in finite iterations. The directions of the master algorithm are generated by only one quadratic programming, and its step-size is always one, the directions of the auxiliary algorithm are new “second-order” feasible descent. Under suitable assumptions, the algorithm is proved to possess global and strong convergence, superlinear and quadratic convergence. Supported by the National Natural Science Foundation of China (19801009) and by the Natural Science Foundation of Guangxi Provience (19811023 and 9912027).