On Semidefinite Programming Relaxations of the Traveling Salesman Problem

Erratum: On Semidefinite Programming Relaxations of the Traveling Salesman Problem

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP), that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in the paper: [D. Cvetković, M. Cangalović and V. Kovačević-Vujčić. Semidefinite Programming Methods for the Symmetric Traveling Salesman...

On Semidefinite Programming Relaxations of the Traveling Salesman Problem

We consider a new semidefinite programming (SDP) relaxation of the symmetric traveling salesman problem (TSP), that may be obtained via an SDP relaxation of the more general quadratic assignment problem (QAP). We show that the new relaxation dominates the one in the paper: [D. Cvetković, M. Cangalović and V. Kovačević-Vujčić. Semidefinite Programming Methods for the Symmetric Traveling Salesman...

Semidefinite Relaxations for the Traveling Salesman Problem

New semidefinite programming relaxations for the Linear Ordering and the Traveling Salesman Problem

In 2004 Newman [43] suggested a semidefinite programming relaxation for the Linear Ordering Problem (LOP) that is related to the semidefinite program used in the Goemans-Williamson algorithm to approximate the Max Cut problem [22]. Her model is based on the observation that linear orderings can be fully described by a series of cuts. Newman [43] shows that her relaxation seems better suited for...

Continuous Relaxations for the Traveling Salesman Problem

In this work, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the discrete optimization problem into continuous spaces. We explore multiple embedding techniques – namely, the construction of dynamical flows on the manifold of orthogonal matrices and associated Procrustes approximations of the TSP cost function. In particular, we find that the Procru...