Yang, X. Q.; Zheng, X. Y. Approximate solutions and optimality conditions of vector variational inequalities in Banach spaces. (English) Zbl 1143.58007 J. Glob. Optim. 40, No. 1-3, 455-462 (2008). Authors’ abstract: We introduce and discuss the notion of \(\varepsilon\)-solutions of vector variational inequalities. Using convex analysis and nonsmooth analysis, we provide some sufficient conditions and necessary conditions for a point to be an \(\varepsilon\)-solution of vector variational inequalities. Reviewer: Pavol Quittner (Bratislava) Cited in 17 Documents MSC: 58E35 Variational inequalities (global problems) in infinite-dimensional spaces 58E17 Multiobjective variational problems, Pareto optimality, applications to economics, etc. 90C46 Optimality conditions and duality in mathematical programming Keywords:vector variational inequality; approximate solution; optimality condition PDFBibTeX XMLCite \textit{X. Q. Yang} and \textit{X. Y. Zheng}, J. Glob. Optim. 40, No. 1--3, 455--462 (2008; Zbl 1143.58007) Full Text: DOI References: [1] Chen, G.-Y., Craven, B. D.: Approximate dual and approximate vector variational inequality for multiobjective optimization. J. Austral. Math. Soc. Ser. A 47, 418–423 (1989) · Zbl 0693.90089 · doi:10.1017/S1446788700033139 [2] Clarke, F.H.: Optimization and Nonsmooth Analysis. Les publications CRM, Montreal, Canada, (1989) · Zbl 0727.90045 [3] Giannessi, F.: Vector Variational Inequalities and Vector Equilibria. Mathematical theories. Nonconvex Optimization and its Applications, 38. Kluwer Academic Publishers, Dordrecht, (2000) · Zbl 0952.00009 [4] Goh, C.J., Yang, X.Q.: On scalarization methods for vector variational inequalities. In: by F. Giannessi,(ed) Vector Variational Inequalities and Vector Equilibria, Kluwer Academic Publishers, Dordrecht/Boston/London, 217–232 (2000) · Zbl 0991.49014 [5] Jeyakumar, V.: Convexlike alternative theorems and mathematical programming. Optimization 16, 643–652 (1985) · Zbl 0581.90079 · doi:10.1080/02331938508843061 [6] Rong, W.D.: Epsilon-approximate solutions to vector optimization problems and vector variational inequalities. (Chinese) Nei Monggol Daxue Xuebao Ziran Kexue 23, 5130–518 (1992) · Zbl 1332.90258 [7] Ward, D.E., Lee, G.M.: On relations between vector optimization problems and vector variational inequalities. J. Optim. Theory Appl. 113, 583–596 (2002) · Zbl 1022.90024 · doi:10.1023/A:1015364905959 [8] Yang, X.Q.: Generalized convex functions and vector variational inequalities. J. Optim. Theory Appl. 79, 563–580 (1993) · Zbl 0797.90085 · doi:10.1007/BF00940559 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.