On iterative computation of fixed points and optimization

Fixexd point theory and applications

Yeol Je Cho¹  Ioannis K Argyros²  Saï³ 

[1] Department of Mathematics Education and RINS, Gyeongsang National University, Jinju, Korea;Department of Mathematics Sciences, Cameron University, Lawton, USA;Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia

关键词: fixed point;    the Gauss-Newton method;    majorizing sequences;    convex composite optimization;    semi-local convergence;    47H10;    47J05;    47J25;    65G99;    49M15;    41A29;   

DOI  :  10.1186/s13663-015-0372-8

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, a semi-local convergence analysis of the Gauss-Newton method for convex composite optimization is presented using the concept of quasi-regularity in order to approximate fixed points in optimization. Our convergence analysis is presented first under the L-average Lipschitz and then under generalized convex majorant conditions. The results extend the applicability of the Gauss-Newton method under the same computational cost as in earlier studies such as Li and Ng (SIAM J. Optim. 18:613-642, 2007), Moldovan and Pellegrini (J. Optim. Theory Appl. 142:147-163, 2009), Moldovan and Pellegrini (J. Optim. Theory Appl. 142:165-183, 2009), Wang (Math. Comput. 68:169-186, 1999) and Wang (IMA J. Numer. Anal. 20:123-134, 2000).

【 授权许可】

CC BY