Before revision:  We formulate a cache optimization problem to maximize the sum of utilities over all contents under stationary and ergodic request process, which is non-convex in general . We find that the problem can be reformulated as a convex optimization problem when the inter-request  distribution has a non-increasing hazard rate function.
After revision:  We formulate a cache optimization problem to maximize the sum of utilities over all contents under stationary and ergodic request process, which is non-convex in general but we reformulate it as a convex optimization problem when the inter-request distribution has a non-increasing hazard rate function.