AN OPTIMIZATION PROBLEM RELATED TO NEURAL NETWORKS

Janssen, A.J.E.M., An optimization problem related to neural networks, Information Processing Letters 37 (1991) 155-157. In this paper we relate the problem of finding the maximum of SIGMA-k(n) = 1 \(s, h(k)) \, where h1,..., h(n) is-a-member-of R(m) are given and s is-a-member-of R(m) is constrained by parallel-to s parallel-to = 1, to the basic problem of neural network theory of finding sigma is-a-member-of {- 1, 0, 1}n such that sgn(A-sigma) = sigma, where A is a given positive semi-definite real (n x n)-matrix. As a consequence we obtain certain certain sharpenings of the results in [1].