Solving Multiobjective Linear Set Optimization Problems

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.