A New Superlinearly Convergent Algorithm Of Combining Qp Subproblem With System Of Linear Equations For Constrained Optimization

In this paper, a class of optimization problems with nonlinear inequality constraints is dis-cussed. Based on the ideas of sequential quadratic programming (SQP) algorithms andsequential systems of linear equations (SSLE) algorithms as well as the strongly sub-feasibledirections method, a new superlinearly convergent algorithm without the strict comple-mentarity is proposed. Unlike the previous work, at each iteration, only one quadraticprogramming subproblem and one or two systems of linear equations with a common co-e?cient matrix are solved in our algorithm. Moreover, the initial iteration point can bechosen arbitrarily and the coe?cient matrix is uniformly nonsingular. After finite iterations,only one quadratic programming subproblem and one system of linear equations are neededto be solved at each iteration, and the iteration points always enter into the feasible setof the original problem. With the help of a new line search technique, the new algorithmpossesses global and superlinear convergence under some suitable assumptions without thestrict complementarity. Finally, the results of numerical experiments show that the proposedalgorithm is e?ective. The main contents of this paper are as follows:In Section 1, some of the related ideas and algorithms for solving nonlinear constrainedoptimization problems are recalled, and then the idea of this paper is introduced.In Section 2, the details of our algorithm and its some important properties are given.In Section 3, under some suitable assumptions, the global convergence of the proposedalgorithm is obtained.In Section 4, under some mild assumptions without the strict complementarity, thestrong and superlinear convergence of our algorithm are proved.In Section 5, some numerical experiments are reported, and its results show that thealgorithm is e?ective and promissing.In Section 6, some concluding remarks are given.