Computation of a Unified Graph-Based Rate Optimization Problem

We define a graph-based rate optimization problem and consider its computation, which provides a unified approach to the computation of various theoretical limits, such as the (conditional) graph entropy, rate-distortion functions and capacity-cost functions with two-sided information. Our contributions are twofold. On the theoretical side, we simplify the graph-based problem by constructing explicit graph contractions in some special cases. These efforts reduce the number of decision variables in the optimization problem. Graph characterizations for rate-distortion and capacity-cost functions with two-sided information are simplified by specializing the results. On the computational side, we design an alternating minimization algorithm for the graph-based problem, which deals with the inequality constraint by a flexible multiplier update strategy. Moreover, deflation techniques are introduced, so that the computing time can be largely reduced. Theoretical analysis shows that the algorithm converges to an optimal solution. The accuracy and efficiency of the algorithm are illustrated by numerical experiments.