Continuous dynamical systems that realize discrete optimization on the hypercube

We study the problem of finding a local minimum of a multilinear function E over the discrete set {0, 1}. The search is achieved by a gradient-like system in [0, 1] 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}. Moreover, the gradient-like system connects with interior point methods for linear programming and with the analog neural network studied by Vidyasagar [Vid95] in the same context. AMS subject classifications. 34D20, 90C51.