Time-Varying Semidefinite Programs

We study time-varying semidefinite programs (TV-SDPs), which are whose data (and solutions) functions of time. Our focus is on the setting where vary polynomially with show that under a strict feasibility assumption, restricting solutions to also be polynomial time does not change optimal value TV-SDP. Moreover, by using Positivstellensatz (positive locus theorem) univariate matrices, we best solution given degree TV-SDP can found solving program tractable size. provide sequence dual problems cast as SDPs and give upper bounds (in maximization form). prove boundedness this converges Under same attained. demonstrate efficacy our algorithms maximum-flow problem edge capacities, wireless coverage requirements, biobjective optimization goal approximate Pareto curve in one shot.