Chen, G. Y. Existence of solutions for a vector variational inequality: An extension of the Hartmann-Stampacchia theorem. (English) Zbl 0795.49010 J. Optimization Theory Appl. 74, No. 3, 445-456 (1992). Summary: A vector variational inequality is studied. The paper deals with existence theorems for solutions under convexity assumptions and without convexity assumptions. Cited in 1 ReviewCited in 167 Documents MSC: 49J40 Variational inequalities Keywords:coercivity; vector variational inequality; convexity PDF BibTeX XML Cite \textit{G. Y. Chen}, J. Optim. Theory Appl. 74, No. 3, 445--456 (1992; Zbl 0795.49010) Full Text: DOI References: [1] Giannessi, F.,Theorems of Alternative, Quadratic Programs, and Complementarity Problems, Variational Inequalities and Complementarity Problems, Edited by R. W. Cottle, F. Giannessi, and J. L. Lions, John Wiley and Sons, Chichester, England, pp. 151-186, 1980. · Zbl 0484.90081 [2] Chen, G. Y., andCheng, G. M.,Vector Variational Inequality and Vector Optimization, Lecture Notes in Economics and Mathematical Systems, Springer-Verlag, Heidelberg, Germany, Vol. 285, 1987. [3] Chen, G. Y., andCraven, B. D.,A Vector Variational Inequality and Optimization over an Efficient Set, Zeitschrift f?r Operations Research, Vol. 3, pp. 1-12, 1990. [4] Chen, G. Y., andYang, X. Q.,Vector Complementarity Problem and Its Equivalences with Weak Minimal Element in Ordered Space, Journal of Mathematical Analysis and Applications, Vol. 153, pp. 136-158, 1990. · Zbl 0719.90078 [5] Hartmann, G. J., andStampacchia, G.,On Some Nonlinear Elliptic Differential Functional Equations, Acta Mathematica, Vol. 115, pp. 271-310, 1966. · Zbl 0142.38102 [6] Fan, K.,A Generalization of Tychonoff’s Fixed-Point Theorem, Mathematics Annals, Vol. 142, pp. 305-310, 1961. · Zbl 0093.36701 [7] Ferrero, O.,Theorems of the Alternative for Set-valued Functions in Infinite-Dimensional Spaces, Optimization, Vol. 20, pp. 167-175, 1989. · Zbl 0676.90099 [8] Dugudji, J., andGranas, A.,KKM Maps and Variational Inequalities, Annali dell Scuola Normale Superiore, Pisa, Italy, pp. 679-682, 1979. [9] Bardaro, C., andCappitelli, R.,Some Further Generalizations of the Knoster-Kuratowski-Mazukiewicz Theorem and Minimax Inequalities, Journal of Mathematical Analysis and Applications, Vol. 132, pp. 484-490, 1988. · Zbl 0667.49016 [10] De Luca, M., andMaugeri, A.,Quasi-Variational Inequalities and Applications to Equilibrium Problems with Elastic Demand, Nonsmooth Optimization and Related Topics, Edited by F. H. Clarke, V. F. Demyanov, and F. Giannessi, Plenum, New York, New York, pp. 61-77, 1989. · Zbl 0746.90018 [11] Holmes, R. B.,Geometric Functional Analysis and Its Applications, Springer-Verlag, Heidelberg, Germany, 1975. · Zbl 0336.46001 [12] Martein, L.,Stationary Points and Necessary Conditions in Vector Extremum Problems, Research Report No. 133, Optimization and Operations Research Group, Department of Mathematics, University of Pisa, Pisa, Italy, 1986. [13] Jameson, G.,Ordered Linear Spaces, Springer-Verlag, Heidelberg, Germany, 1970. · Zbl 0196.13401 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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.