We describe a branch-and-bound algorithm for the quadratic assignment problem (QAP) that uses a convex quadratic programming (QP) relaxation to obtain a bound at each node. The QP subproblems are approximately solved using the Frank-Wolfe algorithm, which in this case requires the solution of a linear assignment problem on each iteration. Our branching strategy makes extensive use of dual infor...

In this paper, we investigate the performance of a practical aggregated LiFi-WiFi system with discrete constellation inputs from view. We derive achievable rate expressions for first time. Then, study maximization problem via optimizing distribution and power allocation jointly. Specifically, multilevel mercy-filling scheme is proposed by exploiting relationship between mutual information minim...

In this paper, we introduce a new method for the problem of unsupervised dependency parsing. Most current approaches are based on generative models. Learning the parameters of such models relies on solving a non-convex optimization problem, thus making them sensitive to initialization. We propose a new convex formulation to the task of dependency grammar induction. Our approach is discriminativ...

The solutions used to solve bi-level congestion pricing problems are usually based on heuristic network optimization methods which may not be able to find the best solution for these type of problems. The application of meta-heuristic methods can be seen as viable alternative solutions but so far, it has not received enough attention by researchers in this field. Therefore, the objective of thi...

We consider optimization of geodesically convex objectives over geodesically convex subsets of the manifold of positive definite matrices. In particular, for this task we develop Euclidean and Riemannian Frank-Wolfe (FW) algorithms. For both settings we analyze non-asymptotic convergence rates to global optimality. To our knowledge, these are the first results on Riemannian FW and its convergen...