On the Envelope of a Variational Inequality
Recently, it has been shown that analyzing variational inequalities and their generalizations by means of a separation scheme leads to connection of different topics, such as regularization, penalization, duality, and so on. This has been done by introducing the definition of image of a variational and quasi-variational inequality, and then exploiting the separation approach. Here we extend the definition of image of a variational inequality and make some comments on further investigations.
KeywordsVariational Inequality Equilibrium Problem Minimum Point Extremum Problem Image Space
Unable to display preview. Download preview PDF.
- 3.Giannessi, F., Separation of sets and gap functions for quasi-variational inequalities. Variational inequalities and network equilibrium problems (Erice, 1994), 101–121, Plenum, New York, 1995.Google Scholar
- 4.Giannessi, F. On connections among separation, penalization and regularization for variational inequalities with point-to-set operators, Equilibrium problems with side constraints. Lagrangean theory and duality, II. Rend. Circ. Mat. Palermo, 48 (1997), 137–145.Google Scholar
- 7.Giannessi, F. and Rapcsk, T., Images, separation of sets and extremum problems. Recent trends in optimization theory and applications, 79–106, World Sci. Publ., River Edge, NJ, 1995.Google Scholar
- 13.Quang, P. H., Lagrangian multiplier rules via image space analysis. Nonsmooth optimization: methods and applications (Erice, 1991), 354–365, Gordon and Breach, Montreux, 1992.Google Scholar