Journal of Mathematical Imaging and Vision

, Volume 53, Issue 2, pp 171–181 | Cite as

iPiasco: Inertial Proximal Algorithm for Strongly Convex Optimization



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.


Heavy-ball method Strongly convex optimization Inertial proximal method Convergence analysis 



Thomas Pock acknowledges support from the Austrian science fund (FWF) under the START project BIVISION, No. Y729. Peter Ochs and Thomas Brox acknowledge funding by the German Research Foundation (DFG Grant BR 3815/5-1).


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.University of FreiburgFreiburgGermany
  2. 2.Graz University of TechnologyGrazAustria
  3. 3.Digital Safety & Security DepartmentAIT Austrian Institute of Technology GmbHViennaAustria

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