Journal
NUMERICAL ANALYSIS AND OPTIMIZATION, NAO-III
Volume 134, Issue -, Pages 59-75Publisher
SPRINGER
DOI: 10.1007/978-3-319-17689-5_3
Keywords
Unconstrained optimization; Barzilai and Borwein gradient method; Quadratic function; R-superlinear convergence; Condition number
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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.
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