In this paper, we develop an optimization decomposition framework for cache management under 'BIG' cache abstraction which fully utilizes the cache resources in a cache network. We assign a utility function to each content, and formulate a joint optimization problem to maximize the overall utility of a cache network. We show that this global network utility maximization problem can be decomposed into two sub-problems, the cache allotment problem and object placement problem, which can be solved separately and iteratively. This decoupling enables us to separately optimize the performance objectives from the perspectives of content providers, cache network operators, and users. We provide exact solution to the object placement problem with Poisson and Pareto request interarrival distributions. We also devise a primal-dual algorithm for online content management. We conduct extensive numerical analysis and simulations to evaluate the performance of our optimization decomposition framework, and study the impact of various key factors such as hazard rate functions of the request interarrival distributions and object popularities. We show that our optimization decomposition framework outperform existing heuristic methods.