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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| Veröffentlicht in: | Applied mathematics and computation Jg. 169; H. 1; S. 247 - 277 |
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| Abstract | 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. |
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| AbstractList | 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. |
| Author | Grapsa, T.N. Sotiropoulos, D.G. |
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| Keywords | 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 |
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| SubjectTerms | 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 |
| Title | Optimal centers in branch-and-prune algorithms for univariate global optimization |
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