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On Robust Saddle-Point Criterion in Optimization Problems with Curvilinear Integral Functionals

Author

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Koushik Das

    (Department of Mathematics, Taki Government College, Taki 743429, India)

Abstract

In this paper, we introduce a new class of multi-dimensional robust optimization problems (named ( P ) ) with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Moreover, we define an auxiliary (modified) class of robust control problems (named ( P ) ( b ¯ , c ¯ ) ), which is much easier to study, and provide some characterization results of ( P ) and ( P ) ( b ¯ , c ¯ ) by using the notions of normal weak robust optimal solution and robust saddle-point associated with a Lagrange functional corresponding to ( P ) ( b ¯ , c ¯ ) . For this aim, we consider path-independent curvilinear integral cost functionals and the notion of convexity associated with a curvilinear integral functional generated by a controlled closed (complete integrable) Lagrange 1-form.

Suggested Citation

  • Savin Treanţă & Koushik Das, 2021. "On Robust Saddle-Point Criterion in Optimization Problems with Curvilinear Integral Functionals," Mathematics, MDPI, vol. 9(15), pages 1-13, July.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:15:p:1790-:d:603314
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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.
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    Cited by:

    1. Savin Treanţă, 2022. "Variational Problems and Applications," Mathematics, MDPI, vol. 11(1), pages 1-4, December.

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