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<p>In this paper, we deal with the generalized Fritz-John (FJ) and Karush-Kuhn-Tucker (KKT) optimality conditions defined by Flores-Bazan and Mastroeni for a nonsmooth nonconvex mathematical programming problem in the face of data uncertainty under the robust counterpart. These uncertainties are included in the objective and the constraints. We first provide definitions for the FJ and KKT conditions in this case, then prove alternative-theorems to characterize these definitions. The constraint qualification used in this paper is similar to those in specific case. Our results cover the outcomes of two previous studies: [Flores-Bazan and Mastroeni’s “Characterizing FJ and KKT conditions in nonconvex mathematical programming with applications” (SIAM J. Optim. 25 (2015) 647-676)] and [Koushki and Soleimani-damaneh’s “Characterization of generalized FJ and KKT conditions in nonsmooth nonconvex optimization” (J. Glob. Optim. 76 (2020) 407-431)] as well as the classic case in the literature.</p>

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Characterization of Generalized FJ and KKT Conditions for Robust Optimization

  • 期刊论文

  • 发表日期：

    2025年5月25日

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  • Javad Koushki,
  • Shokouh Shahbeyk

摘要

In this paper, we deal with the generalized Fritz-John (FJ) and Karush-Kuhn-Tucker (KKT) optimality conditions defined by Flores-Bazan and Mastroeni for a nonsmooth nonconvex mathematical programming problem in the face of data uncertainty under the robust counterpart. These uncertainties are included in the objective and the constraints. We first provide definitions for the FJ and KKT conditions in this case, then prove alternative-theorems to characterize these definitions. The constraint qualification used in this paper is similar to those in specific case. Our results cover the outcomes of two previous studies: [Flores-Bazan and Mastroeni’s “Characterizing FJ and KKT conditions in nonconvex mathematical programming with applications” (SIAM J. Optim. 25 (2015) 647-676)] and [Koushki and Soleimani-damaneh’s “Characterization of generalized FJ and KKT conditions in nonsmooth nonconvex optimization” (J. Glob. Optim. 76 (2020) 407-431)] as well as the classic case in the literature.