A superlinearly convergent SQP method without boundedness assumptions on any of the iterative sequences

This paper is aimed to present a new sequential quadratic programming (SQP) algorithm for finding a solution to nonlinear constrained programming problems with weak conditions, where the improved direction can be yielded by solving one quadratic programming (QP), and the correction direction can be obtained by solving another QP. The main characters of the proposed algorithm are as follows. First, by limiting infeasibility of SQP iterates, the boundedness of the iteration sequence can be obtained in the case of the feasible set being nonempty and bounded as well as the constraint functions being convex. Second, global convergence can be proved under Slater constraint qualification (CQ). Furthermore, superlinear convergence can be ensured under suitable conditions. Third, the proposed algorithm is further improved with a bidirectional line search technique. Finally, some numerical experiments are operated to test the proposed algorithms, and the results demonstrate that they are promising.