Version 1
: Received: 6 September 2024 / Approved: 7 September 2024 / Online: 9 September 2024 (09:03:33 CEST)
How to cite:
Upadhyay, B. B.; Singh, S. K.; Stancu-Minasian, I.; Rusu-Stancu, A. M. Robust Optimality and Duality for Nonsmooth Multiobjective Programming Problems with Vanishing Constraints under Data Uncertainty. Preprints2024, 2024090582. https://doi.org/10.20944/preprints202409.0582.v1
Upadhyay, B. B.; Singh, S. K.; Stancu-Minasian, I.; Rusu-Stancu, A. M. Robust Optimality and Duality for Nonsmooth Multiobjective Programming Problems with Vanishing Constraints under Data Uncertainty. Preprints 2024, 2024090582. https://doi.org/10.20944/preprints202409.0582.v1
Upadhyay, B. B.; Singh, S. K.; Stancu-Minasian, I.; Rusu-Stancu, A. M. Robust Optimality and Duality for Nonsmooth Multiobjective Programming Problems with Vanishing Constraints under Data Uncertainty. Preprints2024, 2024090582. https://doi.org/10.20944/preprints202409.0582.v1
APA Style
Upadhyay, B. B., Singh, S. K., Stancu-Minasian, I., & Rusu-Stancu, A. M. (2024). Robust Optimality and Duality for Nonsmooth Multiobjective Programming Problems with Vanishing Constraints under Data Uncertainty. Preprints. https://doi.org/10.20944/preprints202409.0582.v1
Chicago/Turabian Style
Upadhyay, B. B., I.M. Stancu-Minasian and Andreea Mădălina Rusu-Stancu. 2024 "Robust Optimality and Duality for Nonsmooth Multiobjective Programming Problems with Vanishing Constraints under Data Uncertainty" Preprints. https://doi.org/10.20944/preprints202409.0582.v1
Abstract
This article investigates robust optimality and duality for a class of nonsmooth multiobjective programming problems with vanishing constraints under data uncertainty (in short, UNMPVC) via convexificators. Using the properties of convexificators, we introduce generalized standard Abadie constraint qualification (in short, GS-ACQ) for the considered problem UNMPVC. Moreover, we introduce generalized robust version of nonsmooth stationary conditions, namely, weakly stationary point (in short, RW-Stationary), T-stationary point (in short, RT-Stationary), M-stationary point (in short, RM-Stationary) and S-stationary point (in short, RS-Stationary) for UNMPVC. By employing GS-ACQ, we establish that the RS-Stationary is the necessary first-order optimality condition for a local Pareto solution of UNMPVC. Moreover, under generalized convexity assumptions, we establish sufficient optimality criteria for UNMPVC. Furthermore, we formulate the Wolfe-type (in short, WRD) and Mond-Weir-type (in short, MWRD) robust dual models corresponding to the primal problem UNMPVC.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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