On the Discontinuous Infinite-Dimensional Generalized Quasivariational Inequality Problem

P. Cubiotti
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P. Cubiotti: University of Messina

Journal of Optimization Theory and Applications, 2002, vol. 115, issue 1, No 7, 97-111

Abstract: Abstract In this paper, we deal with the following generalized quasivariational inequality problem: given a real normed space E with topological dual E* and two multifunctions G: X→2 X and F: X→2 E*, find $$\left( {\hat x,\hat \phi } \right)$$ ∈X × E* such that $$\hat x \in G\left( {\hat x} \right),{\text{ }}\hat \phi \in F\left( {\hat x} \right),{\text{ }}\left\langle {\hat \phi ,\hat x - y} \right\rangle \leqslant 0,{\text{for all }}y \in G\left( {\hat x} \right).$$ We extend to such infinite-dimensional setting some existence results which have been obtained recently for the special case where E is finite dimensional. In particular, our assumptions do not imply any kind of continuity for the multifunction F.

Keywords: Generalized quasivariational inequalities; affine hull; lower semicontinuity; Hausdorff lower semicontinuity; open lower sections (search for similar items in EconPapers)
Date: 2002
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Citations: View citations in EconPapers (4)

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DOI: 10.1023/A:1019676929916

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