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Lagrange Duality and Saddle Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-infinite Programming Problems with Vanishing Constraints
Version 1
: Received: 18 July 2024 / Approved: 19 July 2024 / Online: 19 July 2024 (10:53:20 CEST)
How to cite:
Upadhyay, B. B.; Sain, S.; Stancu-Minasian, I. Lagrange Duality and Saddle Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-infinite Programming Problems with Vanishing Constraints. Preprints2024, 2024071566. https://doi.org/10.20944/preprints202407.1566.v1
Upadhyay, B. B.; Sain, S.; Stancu-Minasian, I. Lagrange Duality and Saddle Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-infinite Programming Problems with Vanishing Constraints. Preprints 2024, 2024071566. https://doi.org/10.20944/preprints202407.1566.v1
Upadhyay, B. B.; Sain, S.; Stancu-Minasian, I. Lagrange Duality and Saddle Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-infinite Programming Problems with Vanishing Constraints. Preprints2024, 2024071566. https://doi.org/10.20944/preprints202407.1566.v1
APA Style
Upadhyay, B. B., Sain, S., & Stancu-Minasian, I. (2024). Lagrange Duality and Saddle Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-infinite Programming Problems with Vanishing Constraints. Preprints. https://doi.org/10.20944/preprints202407.1566.v1
Chicago/Turabian Style
Upadhyay, B. B., Shivani Sain and Ioan Stancu-Minasian. 2024 "Lagrange Duality and Saddle Point Optimality Conditions for Nonsmooth Interval-Valued Multiobjective Semi-infinite Programming Problems with Vanishing Constraints" Preprints. https://doi.org/10.20944/preprints202407.1566.v1
Abstract
In this article, we consider a class of nonsmooth interval-valued multiobjective semi-infinite programming problems with vanishing constraints (in short, NIMSIPVC). We introduce the VC-Abadie constraint qualification (in short, VC-ACQ) for NIMSIPVC and employ it to establish Karush-Kuhn-Tucker (in short, KKT)-type necessary optimality conditions. Related to NIMSIPVC, we formulate interval-valued vector Lagrange type dual and scalarized Lagrange type dual problems. Subsequently, we establish weak, strong, and converse duality results relating NIMSIPVC and corresponding dual problems. In addition, we introduce the notions of saddle points for interval-valued vector Lagrangian and scalarized Lagrangian of NIMSIPVC. Moreover, we establish the saddle point optimality criteria for NIMSIPVC. Various non-trivial examples are provided to demonstrate the validity of established results. To the best of our knowledge, optimality conditions, Lagrange type duality, and saddle point optimality criteria for NIMSIPVC have not been investigated yet via Clarke subdifferentials.
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.
