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

Savin Treanţă and Koushik Das
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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

Mathematics, 2021, vol. 9, issue 15, 1-13

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.

Keywords: Lagrange 1-form; second-order Lagrangian; normal weak robust optimal solution; modified objective function method; robust saddle-point (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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