A new feasible descent algorithm combining SQP with generalized projection for optimization problems without strict complementarity

In this paper, optimization problems with nonlinear inequality constraints are discussed, by combining the sequential quadratic programming (SQP) with an new generalized projection technique, a new feasible descent algorithm for solving the problems is presented. At each iteration of the new algorithm, a convex quadratic program (QP) is solved and a master direction is obtained, and an improved (feasible descent) direction is yielded by updating the master direction with an explicit formula, and in order to avoid the Maratos effect, a height-order correction direction is computed by another explicit formula of the master direction and the improved direction, both this two correction formulas contain a new generalized projection technique. Under weaker conditions without the strict complementarity, the new algorithm is proved to possess global convergence and superlinear convergence. Furthermore, the quadratic convergence rate of the algorithm is obtained when the twice derivatives of the objective function and constrained functions are adopted.