Limit vector variational inequality problems via scalarization

M. Bianchi, Igor Konnov () and R. Pini ()
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M. Bianchi: Università Cattolica del Sacro Cuore
R. Pini: Università degli Studi Milano-Bicocca

Journal of Global Optimization, 2018, vol. 72, issue 3, No 10, 579-590

Abstract: Abstract We solve a general vector variational inequality problem in a finite—dimensional setting, where only approximation sequences are known instead of exact values of the cost mapping and feasible set. We establish a new equivalence property, which enables us to replace each vector variational inequality with a scalar set-valued variational inequality. Then, we approximate the scalar set-valued variational inequality with a sequence of penalized problems, and we study the convergence of their solutions to solutions of the original one.

Keywords: Vector variational inequality; Non-stationarity; Set-valued mappings; Approximation sequence; Penalty method; Coercivity conditions (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10898-018-0657-7

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