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Singular Optimization Problems and p-Factor Approach for Their Analysis

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Optimization and Applications (OPTIMA 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 15218))

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Abstract

The paper is devoted to the optimization problems with equality constraints in the case when the Lagrange multiplier associated with the objective function might be equal to zero. We introduce a new modified Lagrange system that has a singular solution of the original optimization problem as its regular solution. We obtain conditions under which this solution is a regular locally unique solution of the modified Lagrange system. Our results are based on constructions of the p-regularity theory and the structure of the p-factor.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Miami University, Oxford, OH, 45056, USA

    Olga Brezhneva

  2. FRC CSC RAS, Vavilov Street 40, 119333, Moscow, Russia

    Yuri Evtushenko, Vlasta Malkova & Alexey Tret’yakov

  3. Systems Research Institute Polish Academy of Sciences, Newelska 6, 01-447, Warsaw, Poland

    Alexey Tret’yakov

  4. Faculty of Sciences, Siedlce University, 08-110, Siedlce, Poland

    Alexey Tret’yakov

Authors
  1. Olga Brezhneva
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  2. Yuri Evtushenko
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  3. Vlasta Malkova
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  4. Alexey Tret’yakov
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Corresponding author

Correspondence to Vlasta Malkova .

Editor information

Editors and Affiliations

  1. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia

    Nicholas Olenev

  2. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

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

    Michael Khachay

  5. Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, Moscow, Russia

    Vlasta Malkova

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Brezhneva, O., Evtushenko, Y., Malkova, V., Tret’yakov, A. (2025). Singular Optimization Problems and p-Factor Approach for Their Analysis. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2024. Lecture Notes in Computer Science, vol 15218. Springer, Cham. https://doi.org/10.1007/978-3-031-79119-2_3

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  • DOI: https://doi.org/10.1007/978-3-031-79119-2_3

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  • Online ISBN: 978-3-031-79119-2

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