Geodesic
Bounds on Eigenvalues of Real Symmetric Interval Matrices for αBB Method in Global Optimization
Yugoslav journal of operations research, Tome 34 (2024) no. 1, p. 73 .

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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.
Classification : 65G40 65F15
Keywords: Global optimization, αBB method, eigenvalues bounds, Hessian matrix, interval matrices, interval analysis 
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     title = {Bounds on {Eigenvalues} of {Real} {Symmetric} {Interval} {Matrices} for {\ensuremath{\alpha}BB} {Method} in {Global} {Optimization}},
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Djamel Zerrouki; Mo; and Ouanes. Bounds on Eigenvalues of Real Symmetric Interval Matrices for αBB Method in Global Optimization. Yugoslav journal of operations research, Tome 34 (2024) no. 1, p. 73 . http://geodesic.mathdoc.fr/item/YJOR_2024_34_1_a3/