A note on Minty type vector variational inequalities

 Access to full text

 Full (PDF)

1. [1] C. Baiocchi and A. Capelo, Variational and Quasivariational Inequalities, Applications to Free-Boundary Problems. John Wiley & Sons, New York (1984). Zbl0551.49007MR745619
2. [2] G.P. Crespi, I. Ginchev and M. Rocca, Minty vector variational inequality, efficiency and proper efficiency. Vietnam J. Math. 32 (2004) 95–107. Zbl1056.49009
3. [3] G.P. Crespi, I. Ginchev and M. Rocca, Variational inequalities in vector optimization, in Variational Analysis and Applications, Series: Nonconvex Optimization and its Applications 79, edited by F. Giannessi and A. Maugeri. Springer, New York (2005), Part II, 259–278. Zbl1132.90015
4. [4] G.P. Crespi, I. Ginchev and M. Rocca, Minty variational inequalities, increase along rays property and optimization. J. Optim. Theory Appl. 123 (2004) 479–496. Zbl1059.49010
5. [5] G.P. Crespi, I. Ginchev and M. Rocca, Increase-along-rays property for vector functions, Preprint 2004/24, Universitá dell’Insubria, Facoltá di Economia, Varese, 2004, (http://eco.uninsubria.it/dipeco/Quaderni/files/QF2004_24.pdf). Zbl1149.49008
6. [6] F. Giannessi, Theorems of alternative, quadratic programs and complementarity problems, in Variational Inequalities and Complementarity Problems, edited by R.W. Cottle, F. Giannessi and J.-L. Lions, John Wiley & Sons, New York (1980) 151–186. Zbl0484.90081
7. [7] F. Giannessi, On Minty variational principle, in New Trends in Mathematical Programming, edited by F. Giannessi, S. Komlósi, and T. Rapcsák, Kluwer, Dordrecht (1998) 93–99. Zbl0909.90253
8. [8] I. Ginchev, Higher order optimality conditions in nonsmooth vector optimization, in Generalized Convexity, Generalized Monotonicity, Optimality Conditions and Duality in Scalar and Vector Optimization, edited by A. Cambini, B.K. Dass and L. Martein. J. Stat. Manag. Syst. 5 (2002) 321–339. Zbl1079.90596
9. [9] I. Ginchev, A. Guerraggio and M. Rocca, First-order conditions for $C^{0,1}$ constrained vector optimization, in Variational Analysis and Applications, Series: Nonconvex Optimization and its Applications 79, edited by F. Giannessi and A. Maugeri. Springer, New York (2005), Part II, 437–450. Zbl1148.90011
10. [10] J.-B. Hiriart-Urruty, New concepts in nondifferentiable programming, Analyse non convexe. Bull. Soc. Math. France 60 (1979) 57–85. Zbl0469.90071
11. [11] D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications, Academic Press, New York (1980). Zbl0457.35001MR567696
12. [12] A.N. Kolmogorov and S.V. Fomin, Elements of the theory of functions and of functional analysis, Nauka, Moscow (1972) (In Russian). Zbl0235.46001
13. [13] S. Komlósi, On the Stampacchia and Minty variational inequalities, in Generalized Convexity and Optimization for Economic and Financial Decisions, Proc. Verona, Italy, May 28–29, 1998, edited by G. Giorgi and F. Rossi, Pitagora Editrice, Bologna (1999) 231–260. Zbl0989.47055
14. [14] D.T. Luc, Theory of Vector Optimization. Springer-Verlag, Berlin (1989). MR1116766
15. [15] G. Mastroeni, Some remarks on the role of generalized convexity in the theory of variational inequalities, in Generalized Convexity and Optimization for Economic and Financial Decisions. Proc. Verona, Italy, May 28–29, 1998, edited by G. Giorgi and F. Rossi, Pitagora Editrice, Bologna (1999) 271–281. Zbl0989.47056
16. [16] G.J. Minty, On the generalization of a direct method of the calculus of variations. Bull. Amer. Math. Soc. 73 (1967) 314–321. Zbl0157.19103
17. [17] B. Mordukhovich, Stability theory for parametric generalized equations and variational inequalities via nonsmooth analysis. Trans. Amer. Math. Soc. 343 (1994) 609–657. Zbl0826.49008
18. [18] A.M. Rubinov, Abstract Convexity and Global Optimization, Kluwer, Dordrecht (2000). Zbl0985.90074MR1834382
19. [19] H.H. Schaefer, Topological Vector Spaces. The MacMillan Company, New York, London, (1966). Zbl0141.30503MR193469
20. [20] G. Stampacchia, Formes bilinéaires coercitives sur les ensembles convexes. C. R. Acad. Sci. Paris (Groupe 1) 258 (1960) 4413–4416. Zbl0124.06401
21. [21] P.T. Thach and M. Kojima, A generalized convexity and variational inequality for quasi-convex minimization. SIAM J. Optim. 6 (1996) 212–226. Zbl0841.49019
22. [22] X.Q. Yang, Generalized convex functions and vector variational inequalities. J. Optim. Theory Appl. 79 (1993) 563–580. Zbl0797.90085
23. [23] A. Zaffaroni, Degrees of efficiency and degrees of minimality. SIAM J. Control Optim. 42 (2003) 1071–1086. Zbl1046.90084