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Nonlinear proximal decomposition method for convex programming. (English) Zbl 0982.90036
Summary: 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 G. Chen and M. Teboulle [Math. Program. 64, 81-101 (1994; Zbl 0823.90097)] and the nonlinear proximal point algorithm using the Bregman function. An advantage of the proposed method is that, by a suitable choice of the Bregman function, each subproblem becomes essentially the unconstrained minimization of a finite-valued convex function. Under appropriate assumptions, the method is globally convergent to a solution of the problem.
MSC:
90C25Convex programming
49M27Decomposition methods in calculus of variations