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Duality Results for a Class of Constrained Robust Nonlinear Optimization Problems

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania
    Academy of Romanian Scientists, 54 Splaiul Independentei, 050094 Bucharest, Romania
    Fundamental Sciences Applied in Engineering—Research Center (SFAI), University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Tareq Saeed

    (Nonlinear Analysis and Applied Mathematics—Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

In this paper, we establish various results of duality for a new class of constrained robust nonlinear optimization problems. For this new class of problems, involving functionals of (path-independent) curvilinear integral type and mixed constraints governed by partial derivatives of second order and uncertain data, we formulate and study Wolfe, Mond-Weir and mixed type robust dual optimization problems. In this regard, by considering the concept of convex curvilinear integral vector functional , determined by controlled second-order Lagrangians including uncertain data, and the notion of robust weak efficient solution associated with the considered problem, we create a new mathematical context to state and prove the duality theorems. Furthermore, an illustrative application is presented.

Suggested Citation

  • Savin Treanţă & Tareq Saeed, 2022. "Duality Results for a Class of Constrained Robust Nonlinear Optimization Problems," Mathematics, MDPI, vol. 11(1), pages 1-17, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2022:i:1:p:192-:d:1019537
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    References listed on IDEAS

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    1. Hong-Zhi Wei & Chun-Rong Chen & Sheng-Jie Li, 2018. "Characterizations for Optimality Conditions of General Robust Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 177(3), pages 835-856, June.
    2. Ziqiang Lu & Yuanguo Zhu & Qinyun Lu, 2021. "Stability Analysis Of Nonlinear Uncertain Fractional Differential Equations With Caputo Derivative," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 29(03), pages 1-10, May.
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