Limit vector variational inequality problems via scalarization

Monica Bianchi, Rita Pini, I. V. Konnov, R. Pini

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)

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.
Original languageEnglish
Pages (from-to)579-590
Number of pages12
JournalJournal of Global Optimization
Volume72
DOIs
Publication statusPublished - 2018

Keywords

  • Approximation sequence ·
  • Coercivity conditions
  • Penalty method
  • Vector variational inequality

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