Study Of Filter-type Algorithms In Solving Constrained Optimization Problems

In this paper, we study the Filter-type algorithms for constrained optimization problems and the paper is divided into five parts.First, we introduce the model, the basic method of constrained optimization problems and some concepts about the convergence of algorithms. Then we give an analysis on the penalty method and emphasize its shortages. After that, we give a detailed introduction of the backgrounds, current researches on the Filter-type algorithms and the main work of the paper.The second part of the paper chooses the SVM classification in pattern recognition as our practical background. Based on a definite qudratic programming model and by combining the Filter method with the primal-dual interior-point algorithm, we construct the Filter interior-point algorithm for definite qudratic programming. Compared with other SVM agorithms, under some assumptions, the Filter interior-point algorithm can convergent globally. As for the feasibility and convergence of the algorithm, we also give detailed analyses.In the third part, we introduce the Filter method into a wide optimization model—the semidefinite programming(SDP). By solving SDP problems throught a NLP, we construct a new Filter and give a Filter-SQP algorithm for SDP. Under some assumptions, we give a detailed proof on the global convergence of the algorithm.The fourth chapter of the paper chooses games theory as practical background. By analyzing the primal-dual path following short-step algorithm, we give a simple application of interior point method on the matrix games.The last chapter concludes the whole paper and points out the creativities. We also give some prospects about further researches on Filter-type algorithms.