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- Title
BOUNDS ON EIGENVALUES OF REAL SYMMETRIC INTERVAL MATRICES FOR aBB METHOD IN GLOBAL OPTIMIZATION.
- Authors
ZERROUKI, Djamel; OUANES, Mohand
- Abstract
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.
- Subjects
SYMMETRIC matrices; EIGENVALUES; GLOBAL optimization; HESSIAN matrices; MATRIX functions; INTERVAL analysis
- Publication
Yugoslav Journal of Operations Research, 2024, Vol 34, Issue 1, p73
- ISSN
0354-0243
- Publication type
Article
- DOI
10.2298/YJOR230315019Z