Free - Steering Relaxation

Working Papers are interim reports on work of the International Institute for Applied Systems Analysis and have received only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. Abstract We consider dual coordinate ascent methods for minimizing a strictly convex (possibly nondiierentiable) function subject to linear constraints. Such methods are useful in large-scale applications (e.g., entropy maximization, quadratic programming, network ows), because they are simple, can exploit sparsity and in certain cases are highly parallelizable. We establish their global convergence under weak conditions and a free-steering order of relaxation. Previous comparable results were restricted to special problems with separable costs and equality constraints. Our convergence framework uniies to a certain extent the approaches of Bregman, Censor and Lent, De Pierro and Iusem, and Luo and Tseng, and complements that of Bertsekas and Tseng.