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Online Optimization Problems with Functional Constraints Under Relative Lipschitz Continuity and Relative Strong Convexity Conditions

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Mathematical Optimization Theory and Operations Research: Recent Trends (MOTOR 2023)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1881))

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Abstract

In this work, we consider the problem of strongly convex online optimization with convex inequality constraints. A scheme with switching over productive and non-productive steps is proposed for these problems. The convergence rate of the proposed scheme is proven for the class of relatively Lipschitz-continuous and strongly convex minimization problems. Moreover, we study the extensions of the Mirror Descent algorithms that eliminate the need for a priori knowledge of the lower bound on the (relative) strong convexity parameters of the observed functions. Some numerical experiments were conducted to demonstrate the effectiveness of one of the proposed algorithms with a comparison with another adaptive algorithm for convex online optimization problems.

The research was supported by Russian Science Foundation (project No. 21-71- 30005), https://rscf.ru/en/project/21-71-30005/..

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Author information

Authors and Affiliations

  1. Moscow Institute of Physics and Technology, 9 Institutsky lane, Dolgoprudny, 141701, Russia

    Oleg Savchuk, Fedor Stonyakin, Mohammad Alkousa, Rida Zabirova, Alexander Titov & Alexander Gasnikov

  2. V. I. Vernadsky Crimean Federal University, 4 Academician Vernadsky Avenue, Simferopol, 295007, Republic of Crimea, Russia

    Oleg Savchuk & Fedor Stonyakin

  3. HSE University, Moscow, 20 Myasnitskaya street, Moscow, 101000, Russia

    Mohammad Alkousa & Alexander Gasnikov

  4. Institute for Information Transmission Problems RAS, 11 Pokrovsky boulevard, 109028, Moscow, Russia

    Alexander Gasnikov

  5. Caucasus Mathematical Center, Adyghe State University, 208 Pervomaiskaya street, Maykop, Republic of Adygea, 385000, Russia

    Alexander Gasnikov

Authors
  1. Oleg Savchuk
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  2. Fedor Stonyakin
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  3. Mohammad Alkousa
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  4. Rida Zabirova
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  5. Alexander Titov
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  6. Alexander Gasnikov
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Corresponding author

Correspondence to Fedor Stonyakin .

Editor information

Editors and Affiliations

  1. Krasovsky Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    Michael Khachay

  2. Sobolev Institute of Mathematics, Novosibirsk, Russia

    Yury Kochetov

  3. Sobolev Institute of Mathematics, Omsk, Russia

    Anton Eremeev

  4. Melentiev Energy Systems Institute, Irkutsk, Russia

    Oleg Khamisov

  5. Institute of Applied Mathematical Research, Petrozavodsk, Russia

    Vladimir Mazalov

  6. University of Florida, Gainesville, FL, USA

    Panos Pardalos

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Savchuk, O., Stonyakin, F., Alkousa, M., Zabirova, R., Titov, A., Gasnikov, A. (2023). Online Optimization Problems with Functional Constraints Under Relative Lipschitz Continuity and Relative Strong Convexity Conditions. In: Khachay, M., Kochetov, Y., Eremeev, A., Khamisov, O., Mazalov, V., Pardalos, P. (eds) Mathematical Optimization Theory and Operations Research: Recent Trends. MOTOR 2023. Communications in Computer and Information Science, vol 1881. Springer, Cham. https://doi.org/10.1007/978-3-031-43257-6_3

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  • DOI: https://doi.org/10.1007/978-3-031-43257-6_3

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-43256-9

  • Online ISBN: 978-3-031-43257-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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