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The pth-Order Karush-Kuhn-Tucker Type Optimality Conditions for Nonregular Inequality Constrained Optimization Problems

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Optimization and Applications (OPTIMA 2023)

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Abstract

In this paper, we present necessary and sufficient optimality conditions for optimization problems with inequality constraints in the finite dimensional spaces. We focus on the degenerate (nonregular) case when the classical constraint qualifications are not satisfied at a solution of the optimization problem. We present optimality conditions of the Karush-Kuhn-Tucker type under new regularity assumptions. To formulate the optimality conditions, we use the p-factor operator, which is the main construction of the p-regularity theory. The approach of p-regularity used in the paper can be applied to various degenerate nonlinear optimization problems due to its flexibility and generality.

This work was supported by the Russian Foundation for Basic Research, project No. 21-71-30005.

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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. Moscow Institute of Physics and Technology, Moscow, Russia

    Yuri Evtushenko

  4. System Res. Inst., Polish Acad. Sciences, Newelska 6, 01-447, Warsaw, Poland

    Alexey Tret’yakov

  5. Faculty of Exact and Natural 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. FRC CSC RAS, Moscow, Russia

    Nicholas Olenev

  2. FRC CSC RAS, Moscow, Russia

    Yuri Evtushenko

  3. University of Montenegro, Podgorica, Montenegro

    Milojica Jaćimović

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

    Michael Khachay

  5. FRC CSC RAS, Moscow, Russia

    Vlasta Malkova

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Brezhneva, O., Evtushenko, Y., Malkova, V., Tret’yakov, A. (2023). The pth-Order Karush-Kuhn-Tucker Type Optimality Conditions for Nonregular Inequality Constrained Optimization Problems. In: Olenev, N., Evtushenko, Y., Jaćimović, M., Khachay, M., Malkova, V. (eds) Optimization and Applications. OPTIMA 2023. Lecture Notes in Computer Science, vol 14395. Springer, Cham. https://doi.org/10.1007/978-3-031-47859-8_2

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  • DOI: https://doi.org/10.1007/978-3-031-47859-8_2

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  • Publisher Name: Springer, Cham

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  • Online ISBN: 978-3-031-47859-8

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