Research On The Modified SR1 Update Formulas And Their Algorithm Convergence

In this paper,we mainly propose two new modified formulas of SRI,which are based on results of previous studies,and we study the convergence of the algorithms.The article is divided into four chapters:In the first chapter,we describe the advantages and disadvantages of Quasi-Newton SRI and BFGS methods as well as the research on SRI methods in domestic and foreign.In the second chapter,we propose a new modified SRI update formula and analyze the convergence of the quasi-Newton algorithm based on the new modified formula SRI under two different hypothesises respectively.Finally we validate the reasonableness of assumptions and effectiveness of algorithms through experiments.In the third chapter,we propose another new modified SRI update formula and analyze the convergence of the quasi-Newton algorithm based on the new modified SRI.Finally,we show the effectiveness of our new algorithm to solve unconstrained optimization problems of uniformly convex functions and nonuniformly convex func-tions through the experiments.In the fourth chapter,we give a summary of our research in this paper,and give some questions for further research.