Stochastic network optimization with non-convex utilities and costs

This work considers non-convex optimization of time averages of network attributes in a general stochastic network. This includes maximizing a non-concave utility function of the time average throughput vector in a time-varying wireless system, subject to network stability and to an additional collection of time average penalty constraints. We develop a simple algorithm that meets all desired stability and penalty constraints, and, subject to a convergence assumption, yields a time average vector that is a local optimum of the desired utility function. We also consider algorithms that yield ¿local near optimal¿ solutions, where the distance to a local optimum can be made as small as desired with a corresponding tradeoff in average delay. Our solution uses Lyapunov optimization with a combination of stochastic dual and primal-dual techniques. We also discuss the relative advantages and disadvantages of these techniques.