Copositive programming is a relative young field which has evolved into a highly active research area in mathematical optimization. An important line of research is to use semidefinite programming to approximate conic programming over the copositive cone. Two major drawbacks of this approach are the rapid growth in size of the resulting semidefinite programs, and … Read more

On semidefinite programming relaxations of maximum k-section

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 > 2 … Read more

A Comparison of Lower Bounds for the Symmetric Circulant Traveling Salesman Problem

When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare … Read more

Numerical block diagonalization of matrix hBcalgebras with application to semidefinite programming

Semidefinite programming (SDP) is one of the most active areas in mathematical programming, due to varied applications and the availability of interior point algorithms. In this paper we propose a new pre-processing technique for SDP instances that exhibit algebraic symmetry. We present computational results to show that the solution times of certain SDP instances may … Read more