On Approximate Efficiency for Nonsmooth Robust Vector Optimization Problems

Acta Mathematica Scientia volume 40, pages887–902(2020)Cite this article

Abstract

In this article, we use the robust optimization approach (also called the worst-case approach) for finding e-efficient solutions of the robust multiobjective optimization problem defined as a robust (worst-case) counterpart for the considered nonsmooth multiobjective programming problem with the uncertainty in both the objective and constraint functions. Namely, we establish both necessary and sufficient optimality conditions for a feasible solution to be an e-efficient solution (an approximate efficient solution) of the considered robust multiobjective optimization problem. We also use a scalarizing method in proving these optimality conditions.

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Author information

Affiliations

  1. Faculty of Mathematics and Computer Science, University of Łódź, Banacha 22, 90-238, Łódź, Poland

    Tadeusz Antczak

  2. Department of Mathematics, Satish Chandra College, Ballia, 277001, India

    Yogendra Pandey

  3. Department of Mathematics, National Institute of Technology, Aizawl, 796012, Mizoram, India

    Vinay Singh

  4. Department of Mathematics, Banaras Hindu University, Varanasi, 221005, India

    Shashi Kant Mishra

Authors
  1. Tadeusz Antczak
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  2. Yogendra Pandey
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  3. Vinay Singh
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  4. Shashi Kant Mishra
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Corresponding author

Correspondence to Tadeusz Antczak.

Additional information

The research of Yogendra Pandey and Vinay Singh are supported by the Science and Engineering Research Board, a statutory body of the Department of Science and Technology (DST), Government of India, through file no. PDF/2016/001113 and SCIENCE & ENGINEERING RESEARCH BOARD (SERB-DST) through project reference no. EMR/2016/002756, respectively.

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Antczak, T., Pandey, Y., Singh, V. et al. On Approximate Efficiency for Nonsmooth Robust Vector Optimization Problems. Acta Math Sci 40, 887–902 (2020). https://doi.org/10.1007/s10473-020-0320-5

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Key words

  • Robust optimization approach
  • robust multiobjective optimization
  • ε-efficient solution
  • ε-optimality conditions
  • scalarization

2010 MR Subject Classification

  • 90C46
  • 90C29
  • 90C30
  • 49J52