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On a Class of Second-Order PDE&PDI Constrained Robust Modified Optimization Problems

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  • Savin Treanţă

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

Abstract

In this paper, by using scalar multiple integral cost functionals and the notion of convexity associated with a multiple integral functional driven by an uncertain multi-time controlled second-order Lagrangian, we develop a new mathematical framework on multi-dimensional scalar variational control problems with mixed constraints implying second-order partial differential equations (PDEs) and inequations (PDIs). Concretely, we introduce and investigate an auxiliary (modified) variational control problem, which is much easier to study, and provide some equivalence results by using the notion of a normal weak robust optimal solution.

Suggested Citation

  • Savin Treanţă, 2021. "On a Class of Second-Order PDE&PDI Constrained Robust Modified Optimization Problems," Mathematics, MDPI, vol. 9(13), pages 1-9, June.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:13:p:1473-:d:580492
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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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