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Article Dans Une Revue International Journal on Artificial Intelligence Tools Année : 2020

Interval Tests and Contractors Based on Optimality Conditions for Bound-Constrained Global Optimization

Résumé

We study the problem of finding the global optimum of a nonlinear real function over an interval box by means of complete search techniques, namely interval branch-and-bound algorithms. Such an algorithm typically generates a tree of boxes from the initial box by alternating branching steps and contraction steps in order to remove non optimal sub-boxes. In this paper, we introduce a new contraction method that is designed to handle the boundary of the initial box where a minimizer may not be a stationary point. This method exploits the first-order optimality conditions and we show that it subsumes the classical monotonicity test based on interval arithmetic. A new branch-and-bound algorithm has been implemented in the interval solver Realpaver. An extensive experimental study based on a set of standard benchmarks is presented.
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Dates et versions

hal-02874694 , version 1 (19-06-2020)

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Laurent Granvilliers. Interval Tests and Contractors Based on Optimality Conditions for Bound-Constrained Global Optimization. International Journal on Artificial Intelligence Tools, 2020, 29 (03n04), pp.2060001. ⟨10.1142/S0218213020600015⟩. ⟨hal-02874694⟩
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