On the convergence rate improvement of a primal-dual splitting algorithm for solving monotone inclusion problems

Radu Ioan Bot(radu.botmathematik.tu-chemnitz.de)
Ernö Robert Csetnek(robert.csetnekmathematik.tu-chemnitz.de)
Andre Heinrich(andre.heinrichmathematik.tu-chemnitz.de)

Abstract: We present two modified versions of the primal-dual splitting algorithm relying on forward-backward splitting proposed in [21] for solving monotone inclusion problems. Under strong monotonicity assumptions for some of the operators involved we obtain for the sequences of iterates that approach the solution orders of convergence of ${\cal {O}}(\frac{1}{n})$ and ${\cal {O}}(\omega^n)$, for $\omega \in (0,1)$, respectively. The investigated primal-dual algorithms are fully decomposable, in the sense that the operators are processed individually at each iteration. We also discuss the modified algorithms in the context of convex optimization problems and present numerical experiments in image processing and support vector machines classification.

Keywords: maximally monotone operator, strongly monotone operator, resolvent, operator splitting, subdifferential, strongly convex function, convex optimization algorithm, duality

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

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Entry Submitted: 03/12/2013
Entry Accepted: 03/12/2013
Entry Last Modified: 03/12/2013

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