A novel iterative convex approximation method

In this paper, we propose a novel iterative algorithm based on convex approximation for a large class of possibly nonconvex optimization problems. The stationary points of the original problem are found by solving a sequence of successively refined approximate problems. To achieve convergence, the approximate problem only needs to be pseudo-convex while the stepsizes are determined by the exact or successive line search. The proposed method not only includes as special cases a variety of existing methods, for example, the gradient projection method and the Jacobi algorithm, but also leads to new algorithms which enjoy easier implementation and faster convergence speed, as illustrated (both theoretically and numerically) by the example application of the sum capacity computation problem of the MIMO broadcast channel.