TY - GEN
T1 - A positive barzilai-borwein-like stepsize and an extension for symmetric linear systems
AU - Dai, Yu Hong
AU - Al-Baali, Mehiddin
AU - Yang, Xiaoqi
N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2015.
PY - 2015
Y1 - 2015
N2 - The Barzilai and Borwein (BB) gradient method has achieved a lot of attention since it performs much more better than the classical steepest descent method. In this paper, we analyze a positive BB-like gradient stepsize and discuss its possible uses. Specifically, we present an analysis of the positive stepsize for two-dimensional strictly convex quadratic functions and prove the R-superlinear convergence under some assumption. Meanwhile, we extend BB-like methods for solving symmetric linear systems and find that a variant of the positive stepsize is very useful in the context. Some useful discussions on the positive stepsize are also given.
AB - The Barzilai and Borwein (BB) gradient method has achieved a lot of attention since it performs much more better than the classical steepest descent method. In this paper, we analyze a positive BB-like gradient stepsize and discuss its possible uses. Specifically, we present an analysis of the positive stepsize for two-dimensional strictly convex quadratic functions and prove the R-superlinear convergence under some assumption. Meanwhile, we extend BB-like methods for solving symmetric linear systems and find that a variant of the positive stepsize is very useful in the context. Some useful discussions on the positive stepsize are also given.
KW - Barzilai and Borwein gradient method
KW - Condition number
KW - Quadratic function
KW - R-superlinear convergence
KW - Unconstrained optimization
UR - http://www.scopus.com/inward/record.url?scp=84947050729&partnerID=8YFLogxK
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U2 - 10.1007/978-3-319-17689-5_3
DO - 10.1007/978-3-319-17689-5_3
M3 - Conference contribution
AN - SCOPUS:84947050729
SN - 9783319176888
T3 - Springer Proceedings in Mathematics and Statistics
SP - 59
EP - 75
BT - Numerical Analysis and Optimization, NAO-III 2014
A2 - Al-Baali, Mehiddin
A2 - Grandinetti, Lucio
A2 - Purnama, Anton
PB - Springer New York LLC
T2 - 3rd International Conference on Numerical Analysis and Optimization: Theory, Methods, Applications and Technology Transfer, NAOIII-2014
Y2 - 5 January 2014 through 9 January 2014
ER -