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Adaptive Descent Splitting Method for Decomposable Optimization Problems

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Mathematical Optimization Theory and Operations Research (MOTOR 2020)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12095))

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Abstract

We suggest a modified descent splitting method for optimization problems having a special decomposable structure. The proposed modification maintains the basic convergence properties but enables one to reduce computational efforts per iteration and to provide computations in a distributed manner. On the one hand, it consists in component-wise choice of descent directions together with a special threshold control. On the other hand, it involves a simple adaptive step-size choice, which takes into account the problem behavior along the iteration sequence. Preliminary computational tests confirm the efficiency of the proposed modification.

The results of the first author in this work were obtained within the state assignment of the Ministry of Science and Education of Russia, project No. 1.460.2016/1.4. In this work, the authors were also supported by the RFBR grant, project No. 19-01-00431.

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Author information

Authors and Affiliations

  1. Department of System Analysis and Information Technologies, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kazan, Russia

    Igor Konnov

  2. Department of Data Mining and Operations Research, Institute of Computational Mathematics and Information Technologies, Kazan Federal University, Kazan, Russia

    Olga Pinyagina

Authors
  1. Igor Konnov
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  2. Olga Pinyagina
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Corresponding author

Correspondence to Olga Pinyagina .

Editor information

Editors and Affiliations

  1. Sobolev Institute of Mathematics SB RAS, Novosibirsk, Russia

    Alexander Kononov

  2. Krasovsky Institute of Mathematics and Mechanics, Yekaterinburg, Russia

    Michael Khachay

  3. National Research University Higher School of Economics, Nizhny Novgorod, Russia

    Valery A Kalyagin

  4. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Konnov, I., Pinyagina, O. (2020). Adaptive Descent Splitting Method for Decomposable Optimization Problems. In: Kononov, A., Khachay, M., Kalyagin, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research. MOTOR 2020. Lecture Notes in Computer Science(), vol 12095. Springer, Cham. https://doi.org/10.1007/978-3-030-49988-4_9

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