B. B. Upadhyay - Department of Mathematics, Indian Institute of Technology, Patna, India. S. K. Singh - Department of Mathematics, Indian Institute of Technology, Patna, India. I. M. Stancu-Minasian - Gheorghe Mihoc-Caius Iacob, Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, 050711 Bucharest, Romania.
In this article, we investigate the duality theorems for a class of non-smooth semidefinite multiobjective programming problems with equilibrium constraints (in short, NSMPEC) via convexificators. Utilizing the properties of convexificators, we present Wolfe-type (in short, WMPEC) and Mond-Weir-type (in short, MWMPEC) dual models for the problem NSMPEC. Furthermore, we establish various duality theorems, such as weak, strong, and strict converse duality theorems relating to the primal problem NSMPEC and the corresponding dual models, in terms of convexificators. Numerous illustrative examples are furnished to demonstrate the importance of the established results. Furthermore, we discuss an application of semidefinite multiobjective programming problems in approximating K-means-type clustering problems. To the best of our knowledge, duality results presented in this paper for NSMPEC using convexificators have not been explored before.
B. B. Upadhyay, S. K. Singh, I. M. Stancu-Minasian, Duality for non-smooth semidefinite multiobjective programming problems with equilibrium constraints using convexificators, Journal of Nonlinear Sciences and Applications, 17 (2024), no. 3, 128--149
Upadhyay B. B., Singh S. K., Stancu-Minasian I. M. , Duality for non-smooth semidefinite multiobjective programming problems with equilibrium constraints using convexificators. J. Nonlinear Sci. Appl. (2024); 17(3):128--149
Upadhyay, B. B., Singh, S. K., Stancu-Minasian, I. M. . "Duality for non-smooth semidefinite multiobjective programming problems with equilibrium constraints using convexificators." Journal of Nonlinear Sciences and Applications, 17, no. 3 (2024): 128--149
