Hadamard well-posedness of a general mixed variational inequality in Banach space
- 238 Downloads
In this paper, we first introduce the concept of Hadamard well-posedness of a general mixed variational inequality in Banach space. Under some suitable conditions, relations between Levitin–Polyak well-posedness and Hadamard well-posedness of a general mixed variational inequality are studied. We also establish some characterizations of Hadamard well-posedness for a genaral mixed variational inequality. Finally, we derive some conditions under which a general mixed variational inequality is Hadamard well-posed.
KeywordsGeneral mixed variational inequality Levitin–Polyak well-posedness Hadamard well-posedness
Mathematics Subject Classification49J40 49K40 90C31
Unable to display preview. Download preview PDF.
- 1.Tykhonov A.N.: On the stability of the functional optimization problem. USSRJ. Comput. Math. Phys. 6, 631–634 (1966)Google Scholar
- 2.Bednarczuk, E.M.: Well-posedness of optimization problem. In: Jahn, J., Krabs, W.(eds.) Recent Advances and Historical Development of Vector Optimization Problems. Lecture Notes in Economics and Mathematical Systems, vol. 294 pp. 51–61. Springer, Berlin (1987)Google Scholar
- 10.Levitin E.S., Polyak B.T.: Convergence of minimizing sequences in conditional extremum problem. Sov. Math. Dokl. 7, 764–767 (1996)Google Scholar
- 12.Kinderlehrer D., Stampacchia G.: An Introduce to Variational Inequalities and their Applications. Academic Press, New York (1980)Google Scholar
- 14.Lignola, M.B., Morgan, J.: Approximate solutions and α-well-posedness for variational inequalities and Nash equilibria. In: Zaccour, G. (ed) Decision and Control in Management Science, pp. 367–398. Kluwer, Dordrecht (2002)Google Scholar
- 15.Del Prete, I., Lignola, M.B., Morgan, J.: New concepts of well-posedness for optimization problems with variational inequality constraints. J. Inequal. Pure Appl. Math. 4(1), Article 5 (2003)Google Scholar
- 17.Hu S., Papageorgiou N.S.: Handbook of Multivalued Analysis: Theory. Springer, New York (1997)Google Scholar