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Peer-reviewedCC BY 4.0Mathematics

Solving Multiobjective Linear Set Optimization Problems

  • Hsien-Chung Wu1
  1. 1Department of Mathematics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan
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Abstract

This paper establishes an embedding theorem for solving multiobjective linear set optimization problems. By introducing a partial order through this embedding framework, we formally define three solution concepts, which are optimal solution, Pareto optimal solution, and ideally optimal solution. We derive distinct optimality conditions for each solution type. Furthermore, by specifying an appropriate convex cone, we demonstrate that these solutions can be practically computed by solving equivalent conventional linear programming problems using the simplex method.

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Cite

BibTeXRIS
BibTeX
@article{wu2026solving,
  title = {{Solving Multiobjective Linear Set Optimization Problems}},
  author = {Hsien-Chung Wu},
  journal = {Mathematics},
  year = {2026},
  month = oct,
  doi = {10.3390/math14203782},
  url = {https://www.mdpi.com/2227-7390/14/20/3782},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Solving Multiobjective Linear Set Optimization Problems
AU  - Hsien-Chung Wu
PY  - 2026
DA  - 2026/10/18
JO  - Mathematics
DO  - 10.3390/math14203782
UR  - https://www.mdpi.com/2227-7390/14/20/3782
AB  - This paper establishes an embedding theorem for solving multiobjective linear set optimization problems. By introducing a partial order through this embedding framework, we formally define three solution concepts, which are optimal solution, Pareto optimal solution, and ideally optimal solution. We derive distinct optimality conditions for each solution type. Furthermore, by specifying an appropriate convex cone, we demonstrate that these solutions can be practically computed by solving equivalent conventional linear programming problems using the simplex method.
SN  - 2227-7390
ER  -