Page 141 - IJOCTA-15-1
P. 141

Duality for robust multi-dimensional vector variational control problem under invexity

             [6] Jeyakumar, V., Li, G., & Lee, G. M. (2012). Ro-  Fractal and Fractional , 7, 18. https://doi.or
                bust duality for generalized convex programming   g/10.3390/fractalfract7010018
                problems under data uncertainty. Nonlinear Anal-  [17] Zhai, Y., Wang, Q., & Tang, T. (2023). Robust
                ysis, Theory, Methods and Applications, 75, 1362-  duality for robust efficient solutions in uncertain
                1373. https://doi.org/10.1016/j.na.2011.          vector optimization problems. Japan Journal of
                04.006                                            Industrial and Applied Mathematics, 40, 907-928.
             [7] Treant¸˘a, S., & Das, K. (2021). On robust saddle-  https://doi.org/10.1007/s13160-022-00562
                point criterion in optimization problems with     -7
                curvilinear integral functionals. Mathematics, 9,  [18] Hanson, M. A. (1981). On sufficiency of the Kuhn-
                1790. https://doi.org/10.3390/math9151790         Tucker conditions. Journal of Mathematical Anal-
             [8] Treant¸˘a, S. (2021). Robust saddle-point criterion  ysis and Applications, 80, 545-550. https://doi.
                in second-order partial differential equation and  org/10.1016/0022-247X(81)90123-2
                partial differential inequation constrained con-  [19] Mond, B., Chandra, S., & Husain, I. (1988) Dual-
                trol problems. International Journal of Robust    ity for variational problems with invexity. Journal
                and Nonlinear Control, 31, 9282-9293. https:      of Mathematical Analysis and Applications, 134,
                //doi.org/10.1002/rnc.5767                        322-328. https://doi.org/10.1016/0022-247
             [9] Elhia, M., Balatif, O., Boujallal, L., & Rachik, M.  X(88)90026-1
                (2021). Optimal control problem for a tuberculo-  [20] Nahak, C., & Nanda, S. (1996). Duality for multi-
                sis model with multiple infectious compartments   objective variational problems with invexity. Op-
                and time delays. An International Journal of Op-  timization, 36, 235-248. https://doi.org/10.1
                timization and Control: Theories & Applications   080/02331939608844181
                (IJOCTA), 11, 75-91. https://doi.org/10.111   [21] Mititelu, S. (2009). Optimality and duality for in-
                21/ijocta.01.2021.00885                           vex multi-time control problems with mixed con-
            [10] Singh, H. P., Bhatia, S. K., Bahri, Y., & Jain,  straints. Journal of Advanced Mathematical Stud-
                R. (2022). Optimal control strategies to combat   ies, 2, 25-34.
                COVID-19 transmission: A mathematical model
                                                              [22] Gulati, T. R., & Mehndiratta, G. (2010). Opti-
                with incubation time delay. Results in Control
                                                                  mality and duality for second-order multiobjec-
                and Optimization, 9, 100176. https://doi.or
                                                                  tive variational problems. European Journal of
                g/10.1016/j.rico.2022.100176
                                                                  Pure and Applied Mathematics, 3, 786-805.
            [11] Aksoy, N. Y., Celik, E., & Dadas, M. E. (2023).
                                                              [23] Sachdev, G., Verma, K., & Gulati, T. R. (2019).
                The solvability of the optimal control problem
                                                                  Second-order symmetric duality in multiobjective
                for a nonlinear Schr¨odinger equation. An Interna-
                                                                  variational problems. Yugoslav Journal of Opera-
                tional Journal of Optimization and Control: The-
                                                                  tions Research, 29, 295-308. https://doi.org/
                ories & Applications (IJOCTA), 13, 269-276. ht
                                                                  10.2298/YJOR180715019S
                tps://doi.org/10.11121/ijocta.2023.1371
                                                              [24] Singh, V., Ahmad, I., Gupta, S. K., & Al-
            [12] Kostyukova, O., & Tchemisova, T. (2024). Ex-
                                                                  Homidan, S. (2021). Duality for multiobjective
                ploring constraint qualification-free optimality
                                                                  variational problems under second-order (ϕ, ρ)-
                conditions for linear second-order cone program-
                                                                  invexity. Filomat, 35, 605-615. https://doi.or
                ming. An International Journal of Optimization
                                                                  g/10.2298/FIL2102605S
                and Control: Theories & Applications (IJOCTA),
                                                              [25] Dubey, V. P., Kumar, D., Alshehri, H. M., Singh,
                14, 168-182. https://doi.org/10.11121/ijoct
                                                                  J., & Baleanu, D. (2022). Generalized invexity
                a.1421
                                                                  and duality in multiobjective variational prob-
            [13] Mititelu, S¸., & Treant¸˘a, S. (2016). Multiobjective
                                                                  lems involving non-singular fractional derivative.
                fractional variational problem on higher-order jet
                bundles. Communications in Mathematics and        Open Physics, 20, 939-962. https://doi.org/10
                                                                  .1515/phys-2022-0195
                Statistics, 4 , 323-340. https://doi.org/10.1
                007/s40304-016-0087-0                         [26] Jayswal, A., & Arana-Jim´enez, M. (2022). Ro-
            [14] Treant¸˘a, S. (2020). Constrained variational prob-  bust penalty function method for an uncertain
                lems governed by second-order Lagrangians. Ap-    multi-time control optimization problems. Jour-
                plicable Analysis, 99, 1467-1484. https://doi.    nal of Mathematical Analysis and Applications,
                org/10.1080/00036811.2018.1538501                 505, 125453. https://doi.org/10.1016/j.jmaa
            [15] Jayswal, A., Preeti, & Treant¸˘a, S. (2022). Ro-  .2021.125453
                bust Duality for Multi-dimensional Variational  [27] Baranwal, A., Jayswal, A., & Preeti. (2022). Ro-
                Control Problem with Data Uncertainty. Multi-     bust duality for the uncertain multitime control
                dimensional Control Problems: Robust Approach,    optimization problems. International Journal of
                145-165. https://doi.org/10.1007/978-981-1        Robust and Nonlinear Control, 32, 5837-5847.
                9-6561-6_7                                        https://doi.org/10.1002/rnc.6113
            [16] Ritu, Treant¸˘a, S., Agarwal, D., & Sachdev, G.  [28] Antczak, T., & Treant¸˘a, S. (2023). Solving invex
                (2023). Robust efficiency conditions in multiple-  multitime control problems with first-order PDE
                objective fractional variational control problems.  constraints via the absolute value exact penalty
                                                           135
   136   137   138   139   140   141   142   143   144   145   146