joint work with Navid Reyhanian, Hamid Farmanbar
We consider the problem of reserving link capacity/resources in a network in such a way that a given set of scenarios (possibly stochastic) can be supported. In the optimal capacity/resource reservation problem, we choose the reserved link capacities to minimize the reservation cost. This problem reduces to a large nonlinear program, with the number of variables and constraints on the order of the number of links times the number of scenarios. We develop an efficient decomposition algorithm for the problem with a provable convergence guarantee.
Multiple-input multi-output (MIMO) detection is a fundamental problem in modern digital communications. Semidefinite relaxation (SDR) based algorithms are a popular class of approaches to solving the problem. In this talk, we shall first develop two new SDRs for MIMO detection and show their tightness under a sufficient condition. This result answers an open question posed by So in 2010. Then, we shall talk about the tighterness relationship between some existing SDRs for the problem in the literature. Finally, we shall briefly talk about the global algorithm based on the newly derived SDR.