On Approximate Efficiency for Nonsmooth Robust Vector Optimization Problems

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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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