Yugoslav Journal of Operations Research 2024 Volume 34, Issue 1, Pages: 73-92
https://doi.org/10.2298/YJOR230315019Z
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Bounds on eigenvalues of real symmetric interval matrices for αBB method in global optimization
Zerrouki Djamel (Laboratoire de Recherche Opérationnelle et de Mathématiques de la Décision, Faculté des Sciences, Université Mouloud Mammeri de Tizi Ouzou, Tizi-Ouzou, Algeria), djamel.zerrouki@ummto.dz
Ouanes Mohand (Laboratoire de Recherche Opérationnelle et de Mathématiques de la Décision, Faculté des Sciences, Université Mouloud Mammeri de Tizi Ouzou, Tizi-Ouzou, Algeria), mohand.ouanes@ummto.dz
In this paper, we investigate bounds on eigenvalues of real symmetric interval matrices. We present a method that computes bounds on eigenvalues of real symmetric interval matrices. It outperforms many methods developed in the literature and produces as sharp as possible bounds on eigenvalues of real symmetric interval matrices. The aim is to apply the proposed method to compute lower bounds on eigenvalues of a symmetric interval hessian matrix of a nonconvex function in the αBB method and use them to produce a tighter underestimator that improves the αBB algorithm for solving global optimization problems. In the end, we illustrate by example, the comparison of various approaches of bounding eigenvalues of real symmetric interval matrices. Moreover, a set of test problems found in the literature are solved efficiently and the performances of the proposed method are compared with those of other methods.
Keywords: Global optimization, αBB method, eigenvalues bounds, Hessian matrix, interval matrices, interval analysis
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