On nonlinear SOR-like methods, III — Global convergence of SOR, SSOR and USSOR methods for convex problems

1998 ◽  
Vol 15 (1) ◽  
pp. 135-145 ◽  
Author(s):  
Kazuo Ishihara ◽  
Tetsuro Yamamoto
Keyword(s):  
Global Convergence ◽  
Convex Problems

scholarly journals A Truncated Descent HS Conjugate Gradient Method and Its Global Convergence

2009 ◽  
Vol 2009 ◽  
pp. 1-13
Author(s):  
Wanyou Cheng ◽  
Zongguo Zhang
Keyword(s):  
Global Convergence ◽  
Line Search ◽  
Optimization Problems ◽  
Test Problems ◽  
Uniformly Convex ◽  
Convex Problems ◽  
Unconstrained Optimization Problems ◽  
Globally Convergent ◽  
Armijo Line Search ◽  
Numerical Performance

Recently, Zhang (2006) proposed a three-term modified HS (TTHS) method for unconstrained optimization problems. An attractive property of the TTHS method is that the direction generated by the method is always descent. This property is independent of the line search used. In order to obtain the global convergence of the TTHS method, Zhang proposed a truncated TTHS method. A drawback is that the numerical performance of the truncated TTHS method is not ideal. In this paper, we prove that the TTHS method with standard Armijo line search is globally convergent for uniformly convex problems. Moreover, we propose a new truncated TTHS method. Under suitable conditions, global convergence is obtained for the proposed method. Extensive numerical experiment show that the proposed method is very efficient for the test problems from the CUTE Library.

Global Convergence of a Cass of Quasi-Newton Methods on Convex Problems

1987 ◽  
Vol 24 (5) ◽  
pp. 1171-1190 ◽  
Author(s):  
Richard H. Byrd ◽  
Jorge Nocedal ◽  
Ya-Xiang Yuan
Keyword(s):  
Global Convergence ◽  
Newton Methods ◽  
Convex Problems ◽  
Quasi Newton

scholarly journals On convergence of a global search strategy for reverse convex problems

2005 ◽  
Vol 2005 (3) ◽  
pp. 149-164 ◽  
Author(s):  
Alexander Strekalovsky
Keyword(s):  
Global Convergence ◽  
Optimality Conditions ◽  
Search Strategy ◽  
Global Search ◽  
Global Optimality ◽  
Global Optimality Conditions ◽  
Convex Problems ◽  
Reverse Convex

On the base of global optimality conditions for RCP we develop the global search strategy (GSS) and focus on the global convergence of GSS giving a variant of the proof.

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