×

Existence of solutions and star-shapedness in generalized Minty variational inequalities in Banach spaces. (English) Zbl 1183.90476

Summary: The purpose of this paper is to introduce and study generalized Minty variational inequalities in Banach spaces. We consider a problem of vector variational inequalities, referred to as generalized Minty \(VI(f'_{-},K)\), in a real Banach space \(X\), where \(K\) is a nonempty subset of \(X\) and \(f'_{-}\) is the lower Dini directional derivative of a real function \(f\) defined on an open set in \(X\) containing \(K\). The results presented in this paper generalize the corresponding results of G. P. Crespi, I. Ginchev and M. Rocca [J. Glob. Optim. 32, No. 4, 485–494 (2005; Zbl 1097.49007)].

MSC:

90C99 Mathematical programming
74P99 Optimization problems in solid mechanics

Citations:

Zbl 1097.49007
PDF BibTeX XML Cite
Full Text: EuDML