Related DatabasesWeb of Science You must be logged in with an active subscription to view this.Article DataHistorySubmitted: 9 July 2020Accepted: 16 February 2021Published online: 25 May 2021Keywordssemidefinite programming, hybrid numeric-symbolic algorithm, spherical codes, packing problemsAMS Subject Headings52C17, 90C22Publication DataISSN (print): 1052-6234ISSN (online): 1095-7189Publisher...

In this paper we solve a wide rang of Semidefinite Programming (SDP) Problem by using Recurrent Neural Networks (RNNs). SDP is an important numerical tool for analysis and synthesis in systems and control theory. First we reformulate the problem to a linear programming problem, second we reformulate it to a first order system of ordinary differential equations. Then a recurrent neural network...

We derive a new semidefinite programming bound for the maximum k-section problem. For k = 2 (i.e. for maximum bisection), the new bound is least as strong as the well-known bound by Frieze and Jerrum [A. Frieze and M. Jerrum. Improved Approximation Algorithms for MAX k-CUT and MAX BISECTION. Algorithmica, 18(1): 67–81, 1997]. For k ≥ 3 the new bound dominates a bound of Karish and Rendl [S.E. K...

Semidefinite programming relaxations of combinatorial problems date back to the work of Lovász [17] from 1979, who proposed a semidefinite programming relaxation for the maximum stable set problem which now is known as the Lovász theta number. More recently, Goemans and Williamson [9] showed how to use semidefinite programming to provide an approximation algorithm for the maximum-cut problem; t...