L. Huerga Pastor
The notions of proper minimality are introduced with the main intention of providing a depurated set of minimal points, that satisfy better properties following some criteria. One of the first notions of proper minimality was given by Geoffrion (1968), for multiobjective (vector) optimization problems with the Pareto order. Several years later, Henig (1982) proposed an alternative concept of proper minimality for general vector optimization problems, that has been also very used in the literature. It is known that both concepts coincide in the multiobjective optimization setting with the Pareto order. In this talk, we generalize these two concepts by introducing alternative notions of proper minimality in the senses of Henig and Geoffrion in the framework of set optimization with finite dimensional spaces. For this aim, we consider a set order relation with respect to a polyhedral ordering cone. Finally, in this setting, we will see that these two notions are equivalent as well.
Keywords: Set optimization, proper minimality notions, set order relation, polyhedral ordering cone
Scheduled
Continuous Optimization I
June 10, 2025 11:30 AM
MR 3