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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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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DOI: https://doi.org/10.1007/s10473-020-0320-5
Key words
- Robust optimization approach
- robust multiobjective optimization
- ε-efficient solution
- ε-optimality conditions
- scalarization