On the efficient Gerschgorin inclusion usage in the global optimization $$\alpha \hbox {BB}$$ α BB method
作者： Milan Hladík
DOI: 10.1007/S10898-014-0161-7
关键词: Scaling 、 State (functional analysis) 、 Hessian matrix 、 Heuristics 、 Global optimization 、 Alpha (programming language) 、 Mathematical optimization 、 Mathematics 、 Eigenvalues and eigenvectors 、 Global optimization problem 、 Management Science and Operations Research 、 Control and Optimization 、 Applied mathematics 、 Computer Science Applications
摘要: In this paper, we revisit the $$\alpha $$ ? BB method for solving global optimization problems. We investigate optimality of scaling vector used in Gerschgorin's inclusion theorem to calculate bounds on eigenvalues Hessian matrix. propose two heuristics compute a good $$d$$ d , and state three necessary conditions an optimal vector. Since vectors calculated by presented methods satisfy all conditions, they serve as cheap but efficient solutions. A small numerical study shows that are practically always optimal.
springer.com
sci-hub.se 参考文章(42)
Christodoulos A. Floudas, Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications) Deterministic Global Optimization: Theory, Methods and (NONCONVEX OPTIMIZATION AND ITS APPLICATIONS Volume 37) (Nonconvex Optimization and Its Applications). ,(2005)
Siegfried M. Rump, INTLAB — INTerval LABoratory Developments in Reliable Computing. pp. 77- 104 ,(1999) , 10.1007/978-94-017-1247-7_7
Nils Tönshoff, Implementation and Computational Results Modular Machine Tools. pp. 112- 117 ,(1997) , 10.1007/978-3-663-08773-1_12
Christodoulos A. Floudas, Deterministic Global Optimization: Theory, Methods and Applications ,(2010)
P. M. Pardalos, Christodoulos C. A. Floudas, Encyclopedia of Optimization Kluwer Academic Publishers. ,(2006)
Carl D. Meyer, Matrix Analysis and Applied Linear Algebra ,(2010)
Leslie Hogben, Handbook Of Linear Algebra ,(2010)
Tibor Csendes, Developments in Reliable Computing ,(2000)
Eligius M.T. Hendrix, Boglárka G.-Tóth, Introduction to Nonlinear and Global Optimization ,(2008)
Bartlomiej Jacek Kubica, Vladik Kreinovich, From Computing Sets of Optima, Pareto Sets, and Sets of Nash Equilibria to General Decision-Related Set Computations Journal of Universal Computer Science. ,vol. 16, pp. 2657- 2685 ,(2010)