Optimal centers in branch-and-prune algorithms for univariate global optimization

We present an interval branch-and-prune algorithm for computing verified enclosures for the global minimum and all global minimizers of univariate functions subject to bound constraints. The algorithm works within the branch-and-bound framework and uses first order information of the objective funct...

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Bibliographic Details
Published in:Applied mathematics and computation Vol. 169; no. 1; pp. 247 - 277
Main Authors: Sotiropoulos, D.G., Grapsa, T.N.
Format: Journal Article
Language:English
Published: New York, NY Elsevier Inc 01.10.2005
Elsevier
Subjects:
Branch-and-prune
Calculus of variations and optimal control
Exact sciences and technology
Global optimization
Mathematical analysis
Mathematics
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in mathematical programming, optimization and calculus of variations
Numerical methods in optimization and calculus of variations
Optimal centers
Optimal mean value form
Pruning steps
Sciences and techniques of general use
Optimal centers
Global optimization
Optimal mean value form
Pruning steps
Branch-and-prune
Optimal mean value
Optimization method
Numerical method
Computing
Algorithm
Natural selection
Optimal center
Branching process
Applied mathematics
Pruning(tree)
Objective function
Mathematical programming
Branch and prune algorithm
ISSN:0096-3003, 1873-5649
Online Access:Get full text
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Summary:We present an interval branch-and-prune algorithm for computing verified enclosures for the global minimum and all global minimizers of univariate functions subject to bound constraints. The algorithm works within the branch-and-bound framework and uses first order information of the objective function. In this context, we investigate valuable properties of the optimal center of a mean value form and prove optimality. We also establish an inclusion function selection criterion between natural interval extension and an optimal mean value form for the bounding process. Based on optimal centers, we introduce linear (inner and outer) pruning steps that are responsible for the branching process. The proposed algorithm incorporates the above techniques in order to accelerate the search process. Our algorithm has been implemented and tested on a test set and compared with three other methods. The method suggested shows a significant improvement on previous methods for the numerical examples solved.
ISSN:0096-3003
1873-5649
DOI:10.1016/j.amc.2004.10.050