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A primal-dual splitting algorithm for finding zeros of sums of maximally monotone operators

Radu Ioan Bot(radu.bot***at***mathematik.tu-chemnitz.de)
Ernö Robert Csetnek(robert.csetnek***at***mathematik.tu-chemnitz.de)
Andre Heinrich(andre.heinrich***at***mathematik.tu-chemnitz.de)

Abstract: We consider the primal problem of finding the zeros of the sum of a maximally monotone operator with the composition of another maximally monotone operator with a linear continuous operator and a corresponding dual problem formulated by means of the inverse operators. A primal-dual splitting algorithm which simultaneously solves the two problems in finite-dimensional spaces is presented. The scheme uses at each iteration separately the resolvents of the maximally monotone operators involved and it gives rise to a splitting algorithm for finding the zeros of the sum of compositions of maximally monotone operators with linear continuous operators. The iterative schemes are used for solving nondifferentiable convex optimization problems arising in image processing and in location theory.

Keywords: maximally monotone operator, resolvent, operator splitting, subdifferential, minimization algorithm, duality

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )


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Entry Submitted: 06/26/2012
Entry Accepted: 06/26/2012
Entry Last Modified: 06/26/2012

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