Smoothing SQP algorithm for semismooth equations with box constraints

In this paper, in order to solve semismooth equations with box constraints, we present a class of smoothing SQP algorithms using the regularized‐smooth techniques. The main difference of our algorithm from some related literature is that the correspondent objective function arising from the equation system is not required to be continuously differentiable. Under the appropriate conditions, we prove the global convergence theorem, in other words, any accumulation point of the iteration point sequence generated by the proposed algorithm is a KKT point of the corresponding optimization problem with box constraints. Particularly, if an accumulation point of the iteration sequence is a vertex of box constraints and additionally, its corresponding KKT multipliers satisfy strictly complementary conditions, the gradient projection of the iteration sequence finitely terminates at this vertex. Furthermore, under local error bound conditions which are weaker than BD‐regular conditions, we show that the proposed algorithm converges superlinearly. Finally, the promising numerical results demonstrate that the proposed smoothing SQP algorithm is an effective method.