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Persistent URL http://purl.org/net/epubs/work/51570
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Record Id 51570
Title On the complexity of steepest descent, Newton’s method and regularized Newton methods for nonconvex unconstrained optimization
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Abstract It is shown that the steepest descent and Newton's method for unconstrained nonconvex optimization under standard asumptions may require numbers of iterations and function evaluations arbitrarily close to O(e-2) to drive the norm of the gradient below e. This shows that the upper bound of O(e-2) evaluations known for the steepest descent method is tight, and that Newton's method may be as slow as steepest descent in the worst case. the improved evaluation complexity bound of O(e-3/2) evaluations known for cubically-regularised Newton methods is also shown to be tight.
Organisation CSE , CSE-NAG , STFC
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Language English (EN)
Type Details URI(s) Local file(s) Year
Report RAL Technical Reports RAL-TR-2009-023. 2009. cgtRALTR2009023.pdf 2009
Journal Article SIAM J Optimiz 20, no. 6 (2010): 2833-2852. 2010
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