An extension of the simplex method to constrained nonlinear optimization
type: Item
instance of: scholarly article
title: An extension of the simplex method to constrained nonlinear optimization
zbMATH Open document ID: 0651.90062
DOI: 10.1007/BF00941060
published in: Journal of Optimization Theory and Applications
publication date: 1989-01-01T00:00:00Z
review text: The simplex algorithm of \textit{J. A. Nelder} and \textit{R. Mead} [Computer J. 7, 308-313 (1965; Zbl 0229.65053)] is extended to handle nonlinear optimization problems with constraints. To prevent the simplex from collapsing into a subspace near the constraints, a delayed reflection is introduced for those points moving into the infeasible region. Numerical experience indicates that the proposed algorithm yields good results in the presence of both inequality and equality constraints, even when the constraint region is narrow. We note that it may be possible to modify and improve the algorithm by trying out variants.
Mathematics Subject Classification ID: 90C30
Mathematics Subject Classification ID: 65K05
Mathematics Subject Classification ID: 49M37
zbMATH DE Number: 4062830
zbMATH Keywords: function minimization
zbMATH Keywords: constrained optimization
zbMATH Keywords: Nelder-Mead simplex algorithm
zbMATH Keywords: delayed reflection
zbMATH Keywords: inequality and equality constraints
author: M. Bala Subrahmanyam
MaRDI profile type: Publication
cites work: Sequential Application of Simplex Designs in Optimisation and Evolutionary Operation
cites work: A Simplex Method for Function Minimization
cites work: A New Method of Constrained Optimization and a Comparison With Other Methods
cites work: Q4060751
cites work: An accelerated multiplier method for nonlinear programming
cites work: A new augmented Lagrangian function for inequality constraints in nonlinear programming problems
description: scientific article; zbMATH DE number 4062830