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Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition
1999
SIAM Journal on Optimization
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
doi:10.1137/s1052623497315203
fatcat:yldulfbxh5ci3jriu4yi3rrwa4