Proximal primal–dual best approximation algorithm with memory

E. M. Bednarczuk (), A. Jezierska () and K. E. Rutkowski ()
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E. M. Bednarczuk: Polish Academy of Sciences
A. Jezierska: Polish Academy of Sciences
K. E. Rutkowski: Warsaw University of Technology

Computational Optimization and Applications, 2018, vol. 71, issue 3, No 7, 767-794

Abstract: Abstract We propose a new modified primal–dual proximal best approximation method for solving convex not necessarily differentiable optimization problems. The novelty of the method relies on introducing memory by taking into account iterates computed in previous steps in the formulas defining current iterate. To this end we consider projections onto intersections of halfspaces generated on the basis of the current as well as the previous iterates. To calculate these projections we are using recently obtained closed-form expressions for projectors onto polyhedral sets. The resulting algorithm with memory inherits strong convergence properties of the original best approximation proximal primal–dual algorithm. Additionally, we compare our algorithm with the original (non-inertial) one with the help of the so called attraction property defined below. Extensive numerical experimental results on image reconstruction problems illustrate the advantages of including memory into the original algorithm.

Keywords: Proximal algorithm with memory; Primal–dual algorithm; Best approximation of the Kuhn–Tucker set; Inclusions with maximally monotone operators; Attraction property; Image reconstruction (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10589-018-0031-1

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