References
- D. Chan and J.S. Pang, The generalized quasi variational inequality problems, Math. Oper. Research 7 (1982), 211-222. https://doi.org/10.1287/moor.7.2.211
- Q.H. Ansari, E. Kobis and J.C. Yao, Vector variational inequalities and vector optimization, Springer International Publishing AG, 2018.
- F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.
- S. Dafermos, Exchange price equilibria and variational inequalities, Math. Program. 46 (1990), 391-402. https://doi.org/10.1007/BF01585753
- V.F. Demyanov, Convexification and Concavification of positively homogeneous functions by the same family of linear functions, Report 3 (1994), 802.
- F. Giannessi, Theorems of alternative, quadratic programs and complementarity problems, in Variational Inequality and Complementarity Problems, (ed. by R.W. Cottle, F. Giannessi, and J.L. Lions), John Wiley and Sons, New York, 151-186, 1994.
- M. Golestani and S. Nobakhtian, Convexificator and strong Kuhn-Tucker conditions, Comput. Math. Appl. 64 (2012), 550-557. https://doi.org/10.1016/j.camwa.2011.12.047
- H. Ishibuchi and H. Tanaka, Multiobjective programming in optimization of the interval objective function, European J. Oper. Res. 48 (1990), 219-225. https://doi.org/10.1016/0377-2217(90)90375-L
- M. Jennane, L. El Fadil and E.M. Kalmoun, Interval-valued vector optimization problems involving generalized approximate convexity, Journal of Mathematics and Computer Science 26 (2020), 67-79. https://doi.org/10.22436/jmcs.026.01.06
- M. Jennane, E.M. Kalmoun and L. Lafhim, Optimality conditions for nonsmooth interval-valued and multiobjective semi-infinite programming, RAIRO-Oper Res. 55 (2021), 1-11. https://doi.org/10.1051/ro/2020066
- V. Jeyakumar and D.T. Luc, Nonsmooth calculus, minimality, and monotonicity of convexificators, J. Optim. Theory Appl. 101 (1999), 599-621. https://doi.org/10.1023/A:1021790120780
- F.A. Khan, R.K. Bhardwaj, T. Ram and Mohammed A.S. Tom, On approximate vector variational inequalities and vector optimization problem using convexificator, AIMS Mathematics 7 (2022), 18870-18882. https://doi.org/10.3934/math.20221039
- D. Kinderlehrer and G. Stampacchia, An introduction to variational inequalities and their applications, Academic Press, London, 1980.
- V. Laha and S.K. Mishra, On vector optimization problems and vector variational inequalities using convexifactors, J. Math. Programm. Oper. Res. 66 (2017), 1837-1850.
- K.K. Lai, S.K. Mishra, M. Hassan, J. Bisht and J.K. Maurya, Duality results for interval-valued semiinfinite optimization problems with equilibrium constraints using convexificators, Journal of Inequalities and Applications 128 (2022), 1-18.
- X.F. Li and J.Z. Zhang, Necessary optimality conditions in terms of convexificators in Lipschitz optimization, J. Optim. Theory Appl. 131 (2006), 429-452. https://doi.org/10.1007/s10957-006-9155-z
- X.J. Long and N.J. Huang, Optimality conditions for efficiency on nonsmooth multiobjective programming problems, Taiwanese J. Math. 18 (2014), 687-699.
- D.V. Luu, Necessary and sufficient conditions for efficiency via convexificators, J. Optim Theory Appl. 160 (2014), 510-526. https://doi.org/10.1007/s10957-013-0377-6
- D.V. Luu, Convexifcators and necessary conditions for efficiency, Optim. 63 (2013), 321-335. https://doi.org/10.1080/02331934.2011.648636
- P. Michel and J.P. Penot, A generalized derivative for calm and stable functions, Differ. Integral Equ. 5 (1992), 433-454.
- R.E. Moore, Interval Analysis, Prentice-Hall, Englewood Cliffs, 1966.
- R.E. Moore, Method and Applications of Interval Analysis, SIAM, Philadelphia, 1979.
- B.S. Mordukhovich and Y.H. Shao, On nonconvex subdifferential calculus in Banach spaces, J. Convex Anal. 2 (1995), 211-227.
- R. Osuna-Gomez, B. Hernadez-Jimenez and Y. Chalco-Cano, New efficiency conditions for multiobjective interval-valued programming problems, Inf Sci. 420 (2017), 235-248. https://doi.org/10.1016/j.ins.2017.08.022
- A.D. Singh and B.A. Dar, Optimality conditions in multiobjective programming problems with interval valued objective functions, Control Cybern. 44 (2015), 19-45.
- A.D. Singh and B.A. Dar and D.S. Kim, Sufficiency and duality in non-smooth interval valued programming problems, J Ind Manag. Optim. 15 (2019), 647-665. https://doi.org/10.3934/jimo.2018063
- B.B. Upadhyay, P. Mishra, R.N. Mohapatra and S.K. Mishra, On the applications of nonsmooth vector optimization problems to solve generalized vector variational inequalities using convexificators, Advances in Intelligent Systems and Computing 991 (2020), 660-671. https://doi.org/10.1007/978-3-030-21803-4_66
- H.C. Wu, Duality theory for optimization problems with interval-valued objective functions, J. Optim Theory Appl. 144 (2010), 615-628. https://doi.org/10.1007/s10957-009-9613-5
- J. Zhang, Q. Zheng, X. Ma and L. Li, Relationships between interval-valued vector optimization problems and vector variational inequalities, Fuzzy Optim. Decis. Mak. 15 (2016), 33-55. https://doi.org/10.1007/s10700-015-9212-x