Detection And Remediation Of Stagnation In The Nelder-Mead Algorithm Using A Sufficient Decrease Condition

Detection And Remediation Of Stagnation In The Nelder-Mead Algorithm Using A Sufficient Decrease Condition (1997)

by C. T. Kelley

Venue:	SIAM J. OPTIM
Citations:	21 - 1 self

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Datum	Value	Source
TITLE	Detection And Remediation Of Stagnation In The Nelder-Mead Algorithm Using A Sufficient Decrease Condition	user correction - Legacy Corrections
AUTHOR NAME	C. T. Kelley	user correction
ABSTRACT	The Nelder-Mead algorithm can stagnate and converge to a non-optimal point, even for very simple problems. In this note we propose a test for sufficient decrease which, if passed for the entire iteration, will guarantee convergence of the Nelder-Mead iteration to a stationary point if the objective function is smooth. Failure of this condition is an indicator of potential stagnation. As a remedy we propose a new step, which we call an oriented restart, which reinitializes the simplex to a smaller one with orthogonal edges which contains an approximate steepest descent step from the current best point. We also give results that apply when objective function is a low-amplitude perturbation of a smooth function. We illustrate our results with some numerical examples.	user correction
YEAR	1997	user correction - Legacy Corrections
VENUE	SIAM J. OPTIM	user correction
VENUE TYPE	JOURNAL	INFERENCE
PAGES	43--55	INFERENCE
VOLUME	10	INFERENCE
TECH	Technical report	INFERENCE
CITATIONS	25 found	ParsCit 1.0