Univariate Global Optimization with Multiextremal Non-Differentiable Constraints Without Penalty Functions |
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Authors: | Yaroslav D Sergeyev |
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Institution: | (1) D.E.I.S.— Università della Calabria, Rende (CS), Italy and University of Nizhni Novgorod, Gagarin Av., 23, 87036 Nizhni Novgorod, Russia |
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Abstract: | This paper proposes a new algorithm for solving constrained global optimization problems where both the objective function
and constraints are one-dimensional non-differentiable multiextremal Lipschitz functions. Multiextremal constraints can lead
to complex feasible regions being collections of isolated points and intervals having positive lengths. The case is considered
where the order the constraints are evaluated is fixed by the nature of the problem and a constraint i is defined only over the set where the constraint i−1 is satisfied. The objective function is defined only over the set where all the constraints are satisfied. In contrast
to traditional approaches, the new algorithm does not use any additional parameter or variable. All the constraints are not
evaluated during every iteration of the algorithm providing a significant acceleration of the search. The new algorithm either
finds lower and upper bounds for the global optimum or establishes that the problem is infeasible. Convergence properties
and numerical experiments showing a nice performance of the new method in comparison with the penalty approach are given.
This research was supported by the following grants: FIRB RBNE01WBBB, FIRB RBAU01JYPN, and RFBR 04-01-00455-a. The author
thanks Prof. D. Grimaldi for proposing the application discussed in the paper.
An erratum to this article is available at . |
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Keywords: | global optimization multiextremal constraints Lipschitz functions continuous index functions |
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