Continuous Cubic Formulations for Cluster Detection Problems in Networks

The celebrated Motzkin-Straus formulation for the maximum clique problem provides a nontrivial characterization of the clique number of a graph in terms of the maximum value of a nonconvex quadratic function over a standard simplex. It was originally developed as a way of proving Tur\'{a}n’s theorem in graph theory, but was later used to develop … Read more

A Cutting Plane Method for Risk-constrained Traveling Salesman Problem with Random Arc Costs

This paper considers the risk-constrained stochastic traveling salesman problem with random arc costs. In the context of stochastic arc costs, the deterministic traveling salesman problem’s optimal solutions would be ineffective because the selected route might be exposed to a greater risk where the actual cost can exceed the resource limit in extreme scenarios. We present … Read more