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Connections between Non-Linear Optimization Problems and Associated Variational Inequalities

Author

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
    Academy of Romanian Scientists, 050094 Bucharest, Romania
    Fundamental Sciences Applied in Engineering-Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Tadeusz Antczak

    (Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland)

  • Tareq Saeed

    (Financial Mathematics and Actuarial Science (FMAS)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia)

Abstract

In this paper, by using the invexity (or pseudoinvexity) and Fréchet differentiability of some integral functionals of curvilinear type, we state some relations between the solutions of a new non-linear optimization problem and the associated variational inequality. In order to prove the results derived in this paper, we use the new notion of invex set by considering some given functions. To justify the effectiveness and outstanding applicability of this work, some illustrative examples are provided.

Suggested Citation

  • Savin Treanţă & Tadeusz Antczak & Tareq Saeed, 2023. "Connections between Non-Linear Optimization Problems and Associated Variational Inequalities," Mathematics, MDPI, vol. 11(6), pages 1-12, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1314-:d:1091751
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    References listed on IDEAS

    as
    1. Antczak, Tadeusz, 2004. "(p,r)-Invexity in multiobjective programming," European Journal of Operational Research, Elsevier, vol. 152(1), pages 72-87, January.
    2. Mishra, S. K. & Wang, S. Y. & Lai, K. K., 2005. "Nondifferentiable multiobjective programming under generalized d-univexity," European Journal of Operational Research, Elsevier, vol. 160(1), pages 218-226, January.
    3. Antczak, Tadeusz, 2009. "Exact penalty functions method for mathematical programming problems involving invex functions," European Journal of Operational Research, Elsevier, vol. 198(1), pages 29-36, October.
    4. Allen Klinger, 1967. "Letter to the Editor—Improper Solutions of the Vector Maximum Problem," Operations Research, INFORMS, vol. 15(3), pages 570-572, June.
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