Relationship between nonsmooth vector optimization problem and vector variational inequalities using convexificators

[1] D. Bhatia, A. Gupta, and P. Arora, Optimality via generalized approximate convexity and quasiefficiency, Optim. Lett. 7 (2013), 127–135.

[2] F.H. Clarke, Optimization and Nonsmooth Analysis, Wiley-Interscience, New York, 1983.

[3] V.F. Demyanov, Convexification and Concavification of positively homogeneous functions by the same family of linear functions, Report 3 (1994), no. 802.

[4] V. F. Demyanov, Exhausters and convexificators new tools in nonsmooth analysis, editors. Quasidifferentiability and Related Topics, Kluwer Academic Publishers, Dordrecht, 2000, pp. 85–137.

[5] V.F. Demyanov and V. Jeyakumar, Hunting for a smaller convex subdifferential, J. Glob. Optim. 10 (1997) 305–326.

[6] M. Golestani and S. Nobakhtian, Convexificator and strong Kuhn-Tucker conditions, Comput. Math. Appl. 64 (2012), 550–557.

[7] D. Gupta and A. Mehra, Two types of approximate saddle points, Numer. Funct. Anal. Optim. 29 (2008), 532–550.

[8] A. Gupta, A. Mehra, and D. Bhatia, Approximate convexity in vector optimization, Bull. Aust. Math. Soc. 74 (2006), 207–218.

[9] V. Jeyakumar and D.T. Luc, Nonsmooth calculus, minimality, and monotonicity of convexificators, J. Optim. Theory Appl. 101 (1999), no. 3, 599–621.

[10] B.C. Joshi, On generalized approximate convex functions and variational inequalities, RAIRO-Oper. Res. 55 (2021), S2999–S3008.

[11] F.A. Khan, R.K. Bhardwaj, T. Ram, and M.A.S. Tom, On approximate vector variational inequalities and vector optimization problem using convexificator, AIMS Math. 7 (2022), no. 10, 18870–18882.

[12] 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.

[13] 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, J. Inequal. Appl. 2022 (2022), no. 1, 128.

[14] 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.

[15] X.F. Li and J.Z. Zhang, Stronger Kuhn-Tucker type conditions in nonsmooth multiobjective optimization: locally Lipschitz case, J. Optim. Theory Appl. 127 (2005), 367–388.

[16] X.J. Long and N.J. Huang, Optimality conditions for efficiency on nonsmooth multiobjective programming problems, Taiwanese J. Math. 18 (2014), 687–699.

[17] D.V. Luu, Convexifcators and necessary conditions for efficiency, Optim. 63 (2013), 321–335.

[18] D.V. Luu, Necessary and sufficient conditions for efficiency via convexificators, J. Optim Theory Appl. 160 (2014), 510–526.

[19] S.K. Mishra and V. Laha, On approximately star-shaped functions and approximate vector variational inequalities, J. Optim. Theory Appl. 156 (2013), 278–293.

[20] S. K. Mishra and V. Laha, On Minty variational principle for nonsmooth vector optimization problems with approximate convexity, Optim. Lett. 10 (2016), 577–589.

[21] S.K. Mishra and B.B. Upadhyay, Some relations between vector variational inequality problems and nonsmooth vector optimization problems using quasi efficiency, Positivity 17 (2013), 1071–1083.

[22] B.B. Upadhyay, P. Mishra, R.N. Mohapatra, and S. K. Mishra, On relationships between vector variational inequality and nonsmooth vector optimization problems via strict minimizers, Adv. Nonlinear Var. Inequal. 20 (2017), Paper No. 2.

[23] 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, Adv. Intel. Syst. Comput. 991 (2020), 660–671.

[24] Z. Wang, R. Li and G. Yu, Vector critical points and generalized quasi efficient solutions in nonsmooth multiobjective programming, J. Inequal. Appl. 2008 (2008), no. 1, 184.

[25] X.Q. Yang and X.Y. Zheng, Approximate solutions and optimality conditions of vector variational inequalities in Banach spaces, J. Global Optim. 40 (2008), 455–462.