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Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems

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Abstract

In this paper, we study the relationship among the generalized Minty vector variational-like inequality problem, generalized Stampacchia vector variational-like inequality problem and vector optimization problem for nondifferentiable and nonconvex functions. We also consider the weak formulations of the generalized Minty vector variational-like inequality problem and generalized Stampacchia vector variational-like inequality problem and give some relationships between the solutions of these problems and a weak efficient solution of the vector optimization problem.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia

    S. Al-Homidan

  2. Department of Mathematics, Aligarh Muslim University, Aligarh, India

    Q. H. Ansari

Authors
  1. S. Al-Homidan
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  2. Q. H. Ansari
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Corresponding author

Correspondence to Q. H. Ansari.

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Communicated by F. Giannessi.

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Al-Homidan, S., Ansari, Q.H. Generalized Minty Vector Variational-Like Inequalities and Vector Optimization Problems. J Optim Theory Appl 144, 1–11 (2010). https://doi.org/10.1007/s10957-009-9591-7

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  • DOI: https://doi.org/10.1007/s10957-009-9591-7

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