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Continuous dynamical systems that realize discrete optimization on the hypercube

Absil, P-A and Sepulchre, R (2004) Continuous dynamical systems that realize discrete optimization on the hypercube. Systems and Control Letters, 52. pp. 297-304. ISSN 0167-6911

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Abstract

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. © 2004 Elsevier B.V. All rights reserved.

Item Type: Article
Uncontrolled Keywords: 0-1 programming Gradient-like systems Interior point methods Lyapunov stability Multilinear functions
Subjects: UNSPECIFIED
Divisions: Div F > Control
Depositing User: Cron Job
Date Deposited: 07 Mar 2014 11:28
Last Modified: 08 Dec 2014 02:24
DOI: 10.1016/j.sysconle.2004.02.008