Journal
JOURNAL OF MATHEMATICAL IMAGING AND VISION
Volume 53, Issue 2, Pages 171-181Publisher
SPRINGER
DOI: 10.1007/s10851-015-0565-0
Keywords
Heavy-ball method; Strongly convex optimization; Inertial proximal method; Convergence analysis
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Funding
- Austrian science fund (FWF) under the START project BIVISION [Y729]
- German Research Foundation (DFG) [BR 3815/5-1]
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In this paper, we present a forward-backward splitting algorithm with additional inertial term for solving a strongly convex optimization problem of a certain type. The strongly convex objective function is assumed to be a sum of a non-smooth convex and a smooth convex function. This additional knowledge is used for deriving a worst-case convergence rate for the proposed algorithm. It is proved to be an optimal algorithm with linear rate of convergence. For certain problems this linear rate of convergence is better than the provably optimal worst-case rate of convergence for smooth strongly convex functions. We demonstrate the efficiency of the proposed algorithm in numerical experiments and examples from image processing.
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