Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition
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چکیده
منابع مشابه
Detection and Remediation of Stagnation in the Nelder--Mead Algorithm Using a Sufficient Decrease Condition
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 remed...
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Probably the most popular algorithm for unconstrained minimization for problems of moderate dimension is the Nelder-Mead algorithm published in 1965. Despite its age only limited convergence results exist. Several counterexamples can be found in the literature for which the algorithm performs badly or even fails. A convergent variant derived from the original Nelder-Mead algorithm is presented....
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The Nelder-Mead Algorithm (NMA) is an almost half-century old method for numerical optimization, and it is a close relative of Particle Swarm Optimization (PSO) and Differential Evolution (DE). Geometric Particle Swarm Optimization (GPSO) and Geometric Differential Evolution (GDE) are recently introduced formal generalization of traditional PSO and DE that apply naturally to both continuous and...
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In this paper, we first prove that the expansion and contraction steps of the Nelder-Mead simplex algorithm possess a descent property when the objective function is uniformly convex. This property provides some new insights on why the standard Nelder-Mead algorithm becomes inefficient in high dimensions. We then propose an implementation of the Nelder-Mead method in which the expansion, contra...
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ژورنال
عنوان ژورنال: SIAM Journal on Optimization
سال: 1999
ISSN: 1052-6234,1095-7189
DOI: 10.1137/s1052623497315203