数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (3): 887-902.doi: 10.1007/s10473-020-0320-5

• 论文 • 上一篇    

ON APPROXIMATE EFFICIENCY FOR NONSMOOTH ROBUST VECTOR OPTIMIZATION PROBLEMS

Tadeusz ANTCZAK, Yogendra PANDEY, Vinay SINGH, Shashi Kant MISHRA   

  1. 1 Faculty of Mathematics and Computer Science, University of Lódź, Banacha 22, 90-238 Lódź, Poland;
    2 Department of Mathematics, Satish Chandra College, Ballia 277001, India;
    3 Department of Mathematics, National Institute of Technology, Aizawl-796012, Mizoram, India;
    4 Department of Mathematics, Banaras Hindu University, Varanasi-221005, India
  • 收稿日期:2018-08-15 修回日期:2019-04-18 出版日期:2020-06-25 发布日期:2020-07-17
  • 通讯作者: Tadeusz ANTCZAK E-mail:tadeusz.antczak@wmii.uni.lodz.pl
  • 基金资助:
    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.

ON APPROXIMATE EFFICIENCY FOR NONSMOOTH ROBUST VECTOR OPTIMIZATION PROBLEMS

Tadeusz ANTCZAK, Yogendra PANDEY, Vinay SINGH, Shashi Kant MISHRA   

  1. 1 Faculty of Mathematics and Computer Science, University of Lódź, Banacha 22, 90-238 Lódź, Poland;
    2 Department of Mathematics, Satish Chandra College, Ballia 277001, India;
    3 Department of Mathematics, National Institute of Technology, Aizawl-796012, Mizoram, India;
    4 Department of Mathematics, Banaras Hindu University, Varanasi-221005, India
  • Received:2018-08-15 Revised:2019-04-18 Online:2020-06-25 Published:2020-07-17
  • Contact: Tadeusz ANTCZAK E-mail:tadeusz.antczak@wmii.uni.lodz.pl
  • Supported by:
    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.

摘要: In this article, we use the robust optimization approach (also called the worst-case approach) for finding ε-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 ε-efficient solution (an approximate efficient solution) of the considered robust multiobjective optimization problem. We also use a scalarizing method in proving these optimality conditions.

关键词: Robust optimization approach, robust multiobjective optimization, ε-efficient solution, ε-optimality conditions, scalarization

Abstract: In this article, we use the robust optimization approach (also called the worst-case approach) for finding ε-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 ε-efficient solution (an approximate efficient solution) of the considered robust multiobjective optimization problem. We also use a scalarizing method in proving these optimality conditions.

Key words: Robust optimization approach, robust multiobjective optimization, ε-efficient solution, ε-optimality conditions, scalarization

中图分类号: 

  • 90C46