Font Size: a A A

Research On New Methods For Solving Unconstrained Optimization Problem

Posted on:2009-12-28Degree:MasterType:Thesis
Country:ChinaCandidate:Y J LiFull Text:PDF
GTID:2120360245967990Subject:Operational Research and Cybernetics
Abstract/Summary:PDF Full Text Request
Two classes of effective methods for solving unconstrained optimization problem are conjugate gradient methods and quasi-Newton methods.Conjugate gradient methods are famous for their interation simplicity and low memory requirements.For quasi-Newton methods,the most effective one is the BFGS.Without forming the Hessian matrix,the method only use the objective function and its first-order derivative value.New conjugate gradient algorithms and new BFGS-TYPE algorithms are studied in this thesis.The global convergence of these new algorithms are proved under some mild conditions respectively. Preliminary numerical results show that they are efficient.In Chapter 1,the foundational knowledge and some famous researches about conjugate gradient methods and quasi-Newton methods are recalled.In Chapter 2,a new conjugate gradient method withβk**base onβkDL2andβk2*is proposed.Then the global convergence for this method is proved under the strong Wolfe-Powell conditions.The numerical results show that the new CG method is efficient.In Chapter 3,another new conjugate gradient method with a modifiedβkN(μ)method is proposed,which can ensure the sufficient descent condition independent of line search. And its global convergence is proved with the weak Wolfe-Powell conditions.Preliminary numerical results show that it is efficient.In Chapter 4,based on the new quasi-Newton equation Bk+1sk=yk*=yk+Aksk, where Ak is some matrix proposed by Wei,et al.(2004),new BFGS-TYPE algorithms are proposed.Then their global convergence and superlinear convergence properties are proved. Numerical experiments have been given to show that they are efficient.
Keywords/Search Tags:unconstrained optimization, conjugate gradient method, quasi-Newton method, BFGS-TYPE algorithm, global convergence, superlinear convergence
PDF Full Text Request
Related items