Two Set Scalarizations Based on the Oriented Distance with Variable Ordering Structures: Properties and Application to Set Optimization
Bienvenido Jiménez, Vicente Novo, A. Vílchez · Numerical Functional Analysis and Optimization · 2021
We consider two set relations defined by general variable order structures and some of their properties are studied. These set relations are characterized by using two scalarization functions based on the oriented distance introduced by Ansari, Köbis and Sharma (Optimization 67 (2018), no. 9, 1389-1407). For these functions, several properties are investigated such as monotonicity and invariance and, by introducing new concepts of properness and boundedness for a set, their finitude is derived. Finally, in set optimization with set criterion and general variable order structures, minimal solutions are characterized by using the scalarization functions above mentioned. Illustrative examples are also given along the paper.