Image Space Analysis for Set Optimization Problems with Applications

Yang-Dong Xu (), Cheng-Ling Zhou () and Sheng-Kun Zhu ()
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Yang-Dong Xu: College of Science, Chongqing University of Posts and Telecommunications
Cheng-Ling Zhou: College of Science, Chongqing University of Posts and Telecommunications
Sheng-Kun Zhu: Southwestern University of Finance and Economics

Journal of Optimization Theory and Applications, 2021, vol. 191, issue 1, No 12, 343 pages

Abstract: Abstract In this paper, we consider a set optimization problem with a partial order relation, which is defined by Minkowski difference. By using the image space analysis, we establish the relationships among the set optimization problem, a vector optimization problem and a set-valued optimization with vector criterion related to the image of the set optimization problem. In addition, two nonlinear regular weak separation functions are proposed for the set optimization problem. Based on the two nonlinear regular weak separation functions, saddle point sufficient optimality conditions, gap functions and error bounds for the set optimization problem, are obtained. Finally, we explore some applications of the obtained results to investigate robust multi-objective optimization problems and verify the validity of the results in shortest path problems with data uncertainty and multi-criteria traffic network equilibrium problems with interval-valued cost functions.

Keywords: Set optimization; Image space analysis; Nonlinear regular weak separation function; Optimality condition; Gap function; Error bound (search for similar items in EconPapers)
Date: 2021
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-021-01939-3

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