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Generalized vector variational-like inequalities and vector optimization

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Abstract

In this paper, we consider different kinds of generalized vector variational-like inequality problems and a vector optimization problem. We establish some relationships between the solutions of generalized Minty vector variational-like inequality problem and an efficient solution of a vector optimization problem. We define a perturbed generalized Stampacchia vector variational-like inequality problem and discuss its relation with generalized weak Minty vector variational-like inequality problem. We establish some existence results for solutions of our generalized vector variational-like inequality problems.

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Authors and Affiliations

  1. Department of Mathematics, Aligarh Muslim University, Aligarh, 202 002, India

    Qamrul Hasan Ansari

  2. Department of Mathematics, University of Isfahan, Isfahan, 81745-163, Iran

    Mahboubeh Rezaie & Jafar Zafarani

  3. University of Sheikhbahaee, Isfahan, Iran

    Jafar Zafarani

Authors
  1. Qamrul Hasan Ansari
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  2. Mahboubeh Rezaie
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  3. Jafar Zafarani
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Correspondence to Qamrul Hasan Ansari.

Additional information

In this research, the second and the third author were partially supported by the Center of Excellence for Mathematics, University of Isfahan, Isfahan, Iran.

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Ansari, Q.H., Rezaie, M. & Zafarani, J. Generalized vector variational-like inequalities and vector optimization. J Glob Optim 53, 271–284 (2012). https://doi.org/10.1007/s10898-011-9686-1

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