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On vector variational-like inequalities and vector optimization problems with (G, α)-invexity

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Abstract

The aim of this paper is to study the relationship among Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and vector optimization problem involving (G, α)-invex functions. Furthermore, we establish equivalence among the solutions of weak formulations of Minty vector variational-like inequality problem, Stampacchia vector variational-like inequality problem and weak efficient solution of vector optimization problem under the assumption of (G, α)-invex functions. Examples are provided to elucidate our results.

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Acknowledgements

The authors are greatly indebted to the reviewers for their valuable comments and suggestions leading to the revised version of the original draft for this paper.

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Authors and Affiliations

  1. Department of Applied Mathematics, Indian Institute of Technology (Indian School of Mines), Dhanbad, 826004, Jharkhand, India

    Anurag Jayswal & Sarita Choudhury

  2. Department of Mathematics, Science College (Autonomous), Hinjilicut, Ganjam, 761102, Odisha, India

    Sarita Choudhury

Authors
  1. Anurag Jayswal
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  2. Sarita Choudhury
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Correspondence to Sarita Choudhury.

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Jayswal, A., Choudhury, S. On vector variational-like inequalities and vector optimization problems with (G, α)-invexity. Appl. Math. J. Chin. Univ. 32, 323–338 (2017). https://doi.org/10.1007/s11766-017-3339-1

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  • DOI: https://doi.org/10.1007/s11766-017-3339-1

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