Scalarization and convergence in unified set optimization
Khushboo, C. S. Lalitha · RAIRO - Operations Research · 2021
This paper deals with scalarization and stability aspects for a unified set optimization problem. We provide characterization for a unified preference relation and the corresponding unified minimal solution in terms of a generalized oriented distance function of the sup-inf type. We establish continuity of a function associated with the generalized oriented distance function and provide an existence result for the unified minimal solution. We establish Painlevé–Kuratowski convergence of minimal solutions of a family of scalar problems to the minimal solutions of the unified set optimization problem.