A Globally And Superlinearly Convergent Primal-Dual Interior Point QP-Free Algorithm For General Constrained Optimization

In this paper, a kind of general constrained optimization problem is discussed. Based on a simple penalty parameter and using the idea of primal-dual interior point methods, we solve the constrained optimization with both inequalities and equalities constraints in a feasible QP-free type way. We adopt a technique of " working set " for judging the active set in this thesis. And the algorithm only needs to solve three reduced systems of linear equations with a common coefficient matrix at every iteration. Under mild conditions, the proposed algorithm is globally and superlinearly convergent. Finally, more than 40 numerical results are reported to show that our algorithm is effective. The main content of this paper is as follows:In Section 1, the foundational knowledge about QP-free algorithm and primal-dual interior point methods is introduced.In Section 2, the main algorithm in this paper is established. Then some important properties about this algorithm are obtained.In Section 3, under mild conditions, the global convergence of the proposed algorithm is proved.In Section 4, the strong and superlinear convergence of the proposed algorithm are proved.In Section 5, numerical experiments have been given to show that our algorithm is efficient.