Department of Applied Mathematics & Physics, Kyoto Univiversity

Technical Report #99015 (July, 1999)

Nonlinear proximal decomposition method for convex programming
by Masahiro Kyono and Masao Fukushima

In this paper, we propose a new decomposition method for solving convex programming problems with separable structure. The proposed method is based on the decomposition method proposed by Chen and Teboulle and the nonlinear proximal point algorithm using Bregman function. An advantage of the proposed method is that, by a suitable choice of Bregman function, each subproblem essentially becomes unconstrained minimization of a finite-valued convex function. Under some appropriate assumptions, the method is globally convergent to a solution of the problem.