Stability Index Method for Global Minimization

Dover, James; Gutman, Semion

doi:10.1007/s10898-006-9010-7

Cited by 1 publication

(3 citation statements)

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“…The Stability Index Method described in the previous sections was tested on several functions designed to test and compare various minimization algorithms, see [11] for additional test functions results. The experiments were conducted on a 2.8 GHz PC with 256 MB RAM.…”

Section: Numerical Results For Simmentioning

confidence: 99%

“…In several papers, starting with [14], the authors developed and tested the Stability Index Method (SIM) for global minimization. In our presentation here we follow [11], which also contains a convergence analysis and additional numerical results.…”

Section: Stability Index Methodsmentioning

confidence: 99%

“…Let D R = B R \ D, and S R be the boundary of B R . The estimate 11) and formula (2.10) imply 12) where here and in the sequel c and C denote various constants. Also, using the Cauchy inequality, formula (2.10), inequality (2.11) and the assumption γ > 1, one gets…”

Section: Modified Rayleigh Conjecturementioning

confidence: 99%

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Modified Rayleigh conjecture method and its applications

Ramm

Gutman

2008

Nonlinear Analysis: Theory, Methods & Applications

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The Rayleigh conjecture about convergence up to the boundary of the series representing the scattered field in the exterior of an obstacle D is widely used by engineers in applications. However this conjecture is false for some obstacles. AGR introduced the Modified Rayleigh Conjecture (MRC), which is an exact mathematical result. In this paper we present the theoretical basis for the MRC method for 2D and 3D obstacle scattering problems, for static problems, and for scattering by periodic structures. We also present successful numerical algorithms based on the MRC for various scattering problems. The MRC method is easy to implement for both simple and complex geometries. It is shown to be a viable alternative for other obstacle scattering methods. Various direct and inverse scattering problems require finding global minima of functions of several variables. The Stability Index Method (SIM) combines stochastic and deterministic method to accomplish such a minimization.

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Section: Numerical Results For Simmentioning

confidence: 99%

Section: Stability Index Methodsmentioning

confidence: 99%