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.

翻译：本文定义了一个图基速率优化问题并考虑其计算，为计算多种理论极限（如（条件）图熵、具有双边信息的率失真函数与容量代价函数）提供了统一方法。我们的贡献包含理论计算两个方面。在理论方面，我们通过构造特定情形下的显式图收缩来简化图基问题，这些工作减少了优化问题中的决策变量数量。通过特化相关结果，具有双边信息的率失真与容量代价函数的图特征刻画得到了简化。在计算方面，我们为该图基问题设计了一种交替最小化算法，该算法通过灵活乘子更新策略处理不等式约束。此外，引入紧缩技术可大幅缩减计算时间。理论分析表明该算法收敛于最优解。数值实验验证了算法的精度与效率。