Article (Scientific journals)
Continuous dynamical systems that realize discrete optimization on the hypercube
Absil, P.-A.; Sepulchre, Rodolphe
2004In Systems and Control Letters, 52 (3-4), p. 297-304
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Keywords :
gradient-like systems; multilinear functions; 0-1 programming; interior point methods; Lyapunov stability
Abstract :
[en] We study the problem of finding a local minimum of a multilinear function E over the discrete set {0, 1}(n). The search is achieved by a gradient-like system in [0, 1](n) with cost function E. Under mild restrictions on the metric, the stable attractors of the gradient-like system are shown to produce solutions of the problem, even when they are not in the vicinity of the discrete set {0, 1}(n). Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar (IEEE Trans. Automat. Control 40 (8) (1995) 1359), in the same context. (C) 2004 Elsevier B.V. All rights reserved.
Disciplines :
Computer science
Engineering, computing & technology: Multidisciplinary, general & others
Author, co-author :
Absil, P.-A.;  Université Catholique de Louvain - UCL > INMA
Sepulchre, Rodolphe ;  Université de Liège - ULiège > Dép. d'électric., électron. et informat. (Inst.Montefiore) > Systèmes et modélisation
Language :
English
Title :
Continuous dynamical systems that realize discrete optimization on the hypercube
Publication date :
July 2004
Journal title :
Systems and Control Letters
ISSN :
0167-6911
eISSN :
1872-7956
Publisher :
Elsevier Science Bv, Amsterdam, Netherlands
Volume :
52
Issue :
3-4
Pages :
297-304
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 22 December 2009

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