2469fd8e-9ac2-4a9f-b7d8-d8e57351c59120210218102044137wseamdt@crossref.orgMDT DepositWSEAS TRANSACTIONS ON MATHEMATICS1109-276910.37394/23206http://wseas.org/wseas/cms.action?id=40512720202720201910.37394/23206.2020.19http://wseas.org/wseas/cms.action?id=23185Approximate-Karush-Kuhn-Tucker Conditions and Interval Valued Vector Variational InequalitiesKinKeung LaiCollege of Economics, Shenzhen University, Shenzhen, CHINASanjeev KumarSinghDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, INDIAShashi KantMishraDepartment of Mathematics, Institute of Science, Banaras Hindu University, Varanasi, INDIAThis Article deals with the Approximate Karush-Kuhn-Tucker (AKKT) optimality conditions for interval valued multiobjective function as a generalization of Karush-Kuhn-Tucker optimality conditions. Further, we establish relationship between vector variational inequality problems and multiobjective interval valued optimization problems under the assumption of LU−convex smooth and nonsmooth objective functions.642020642020280288https://www.wseas.org/multimedia/journals/mathematics/2020/a565106-1241.pdf10.37394/23206.2020.19.28https://www.wseas.org/multimedia/journals/mathematics/2020/a565106-1241.pdfL. Fan, S. Liu and S. Gao, Generalized mono-tonicity and convexity of non-differentiable functions, J. Math. Anal. Appl.279, 2003pp. 279–289.10.1016/j.ejor.2005.09.007H. C. Wu, The Karush-Kuhn-Tucker optimality conditions in an optimization problem within terval-valued objective function, European J. Oper. Res.176 (1), 2007 pp. 46–59.10.1016/j.ejor.2008.03.012H. C. Wu, The Karush-Kuhn-Tucker optimality conditions in multi objective programming problems with interval-valued objective functions,European J. Oper. Res.196(1), 2009 pp. 49–60.[4] H. C. Wu, On interval-valued nonlinear programming problems, J. Math. Anal. Appl. 338(1), 2008 pp. 299–316.R. E. Moore,Methods and Applications of Interval Analysis, SIAM Philadelphia 1994. 10.1287/mnsc.16.5.374A. Ben-Israel and P. D. Robers, A decomposition method for interval linear programming, Management Science16(5), 1970 pp. 374–387.F. Giannessi,Theorems of alternative, quadratic programs and complementarity problems, Wiley, Chichester 1980.F. H. Clarke,Optimization and nonsmooth analysis,John Wiley & Sons, Inc., New York 1983.10.1007/s10957-016-0986-yG. Giorgi, B. Jim ́enez and V. Novo, Approximate Karush-Kuhn-Tucker condition in multiobjective optimization, J. Optim. Theory Appl.171,2016 pp. 70–89.10.1007/s10957-011-9802-xG. Haeser and M. Schuverdt, On approximate KKT condition and its extension to continuous variational inequalities, J. Optim. Theory Appl.149, 2011 pp. 528–539.10.1201/b15244-14G. Mastroeni, Some remarks on the role of generalized convexity in the theory of variational inequalities,Generalized convexity and optimization for economic and financial decisions Pitagora, Bologna 1999 pp. 271–281.H. W. Kuhn and A. W. Tucker, Nonlinear programming, University of California Press, Berkeley and Los Angeles 1951.10.1002/cpa.3160200302J.-L. Lions and G. Stampacchia, Variational inequalities, Comm. Pure Appl. Math.20, 1967pp. 493–519.10.1023/a:1024791525441J. M. Martnez and B. F. Svaiter, A practical optimality condition without constraint qualifications for nonlinear programming, J. Optim. Theory Appl.118, 2003 pp. 117–133.M. R. Hestenes,Optimization theory: the finite dimensional case, John Wiley & Sons, New York 1975.10.1137/090777189R. Andreani, J. M. Mart ́ınez and B. F. Svaiter, A new sequential optimality condition for con-strained optimization and algorithmic consequences,SIAM J. Optim. 20, 2010 pp. 3533–3554.10.1080/02331930903578700R. Andreani, G. Haeser and J. M. Mart ınez, On sequential optimality conditions for smooth constrained optimization,Optimization60, 2011pp. 627–641.10.1080/02331934.2016.1250268V. Laha and S. K. Mishra, On vector optimization problems and vector variational inequalities using convexificators, Optimization66, 2017, pp. 1837–1850.10.1007/s10700-015-9212-xJ. Zhang, Q. Zheng, X. Ma and L. Li, Relation-ships between intervalvalued vector optimization problems and vector variational inequalities,Fuzzy Optim. Decis. Making15, 2016 pp. 33–55.