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Zbl 0982.90036
Kyono, M.; Fukushima, M.
Nonlinear proximal decomposition method for convex programming. (English)
[J] J. Optimization Theory Appl. 106, No.2, 357-372 (2000). ISSN 0022-3239; ISSN 1573-2878/e

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 {\it G. Chen} and {\it 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 2000:: *90C25 Convex programming
49M27 Decomposition methods

Keywords: nonlinear proximal decomposition method; bregman functions; convex programming; nonlinear proximal point algorithm

Citations: Zbl 0823.90097

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