Characterization of set order relations and set optimization problems via conic scalarization

Madhusudan Das (), Debdas Ghosh (), Jen-Chih Yao () and Xiaopeng Zhao ()
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Madhusudan Das: China Medical University, Research Center for Interneural Computing
Debdas Ghosh: Indian Institute of Technology (BHU), Department of Mathematical Sciences
Jen-Chih Yao: China Medical University, Research Center for Interneural Computing
Xiaopeng Zhao: Tiangong University, School of Mathematical Sciences

Journal of Global Optimization, 2025, vol. 93, issue 3, No 6, 777-801

Abstract: Abstract In this paper, we employ Kasimbeyli’s conic scalarization function and relax certain conditions from the existing literature to provide an equivalent scalar representation of set order relations in normed spaces. Furthermore, we apply these results to derive optimality conditions for set-valued optimization problems. By introducing suitable sets and a convex cone in the image space, we establish optimality conditions for various concepts of robust solutions for uncertain multiobjective optimization problems. Several examples are given to illustrate the accuracy and usefulness of the results.

Keywords: Set optimization; Set order relations; Conic scalarization; Optimality conditions; Uncertain multi-objective optimization; 49J53; 90C26; 90C46; 65K10 (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10898-025-01546-w

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