Distributed Algorithm for Nonconvex Power Optimization: Achieving Global Weighted Sum-Rate Maximum

A majority of network-level utility optimization problem can be formulated as, transformed or reduced to a nonconvex Weighted Sum-Rate Maximization (WSRM) problem with respect to power optimization, which plays central role on the ultimate performance of a network. However, achieving global WSRM through distributed approach has been a long standing open problem in interference-coupled networks. This paper creates a distributed global power optimization algorithm for WSRM, which arguably represents the first effort to realize distributed WSRM by jointly exploiting the both virtues of monotonic optimization and nonlinear Perron-Frobenius theory. Benefiting from the nonlinear Perron-Frobenius theory, we derive a distributed projection algorithm at the heart of outer polyblock approximation method developed from monotonic optimization. Such a distributed projection allows each link (user) to generate a consensus about shrinking polyblock relying on nothing more than local measurements of SINR, which will greatly facilitates practical implementation. The shrinking polyblock approximates to the noncovex feasible region with respect to link rate, then we can arrive at the global optimum of WSRM by searching over the vertex set of the convergent polyblock instead of original region. Additionally and remarkably, the well-designed projection algorithm exhibits geometrical convergence rate, which will significantly expedite WSRM by reducing the computation complexity.