## 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

Zbl 1097.49007
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