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Proximal primal–dual best approximation algorithm with memory

Abstrakt

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.

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Informacje szczegółowe

Kategoria:
Publikacja w czasopiśmie
Typ:
artykuły w czasopismach
Opublikowano w:
COMPUTATIONAL OPTIMIZATION AND APPLICATIONS nr 71, strony 767 - 794,
ISSN: 0926-6003
Język:
angielski
Rok wydania:
2018
Opis bibliograficzny:
Bednarczuk E., Węsierska A., Rutkowski K.: Proximal primal–dual best approximation algorithm with memory// COMPUTATIONAL OPTIMIZATION AND APPLICATIONS -Vol. 71,iss. 3 (2018), s.767-794
DOI:
Cyfrowy identyfikator dokumentu elektronicznego (otwiera się w nowej karcie) 10.1007/s10589-018-0031-1
Weryfikacja:
Politechnika Gdańska

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