Constrained global optimization of multivariate polynomials using Bernstein branch and prune algorithm

We propose an algorithm for constrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems. The proposed Bernstein branch and prune algorithm is based on the Bernstein polynomial approach. We introduce several new features in this proposed algorithm to ma...

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Bibliographic Details
Published in:Journal of global optimization Vol. 49; no. 2; pp. 185 - 212
Main Authors: Nataraj, P. S. V., Arounassalame, M.
Format: Journal Article
Language:English
Published: Boston Springer US 01.02.2011
Springer Nature B.V
Subjects:
Algorithms
Computer Science
Mathematical programming
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Polynomials
Propagation
Real Functions
Studies
Pruning
Constrained global optimization
Subdivision
Bernstein polynomials
ISSN:0925-5001, 1573-2916
Online Access:Get full text
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Summary:We propose an algorithm for constrained global optimization to tackle non-convex nonlinear multivariate polynomial programming problems. The proposed Bernstein branch and prune algorithm is based on the Bernstein polynomial approach. We introduce several new features in this proposed algorithm to make the algorithm more efficient. We first present the Bernstein box consistency and Bernstein hull consistency algorithms to prune the search regions. We then give Bernstein contraction algorithm to avoid the computation of Bernstein coefficients after the pruning operation. We also include a new Bernstein cut-off test based on the vertex property of the Bernstein coefficients. The performance of the proposed algorithm is numerically tested on 13 benchmark problems. The results of the tests show the proposed algorithm to be overall considerably superior to existing method in terms of the chosen performance metrics.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-009-9485-0