A variant of SQP method for inequality constrained optimization and its global convergence

In this paper, a variant of SQP method for solving inequality constrained optimization is presented. This method uses a modified QP subproblem to generate a descent direction as each iteration and can overcome the possible difficulties that the QP subproblem of the standard SQP method is inconsistency. Furthermore, the method can start with an infeasible initial point. Under mild conditions, we prove that the algorithm either terminates as KKT point within finite steps or generates an infinite sequence whose accumulation point is a KKT point or satisfies certain first-order necessary condition. Finally, preliminary numerical results are reported.