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Limit vector variational inequality problems via scalarization

Author

Listed:
  • M. Bianchi

    (Università Cattolica del Sacro Cuore)

  • I. V. Konnov

    (Kazan Federal University)

  • R. Pini

    (Università degli Studi Milano-Bicocca)

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.

Suggested Citation

  • M. Bianchi & I. V. Konnov & R. Pini, 2018. "Limit vector variational inequality problems via scalarization," Journal of Global Optimization, Springer, vol. 72(3), pages 579-590, November.
    • Handle: RePEc:spr:jglopt:v:72:y:2018:i:3:d:10.1007_s10898-018-0657-7
    DOI: 10.1007/s10898-018-0657-7
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