Henri Bonne†‡
Abstract: The paper deals with semivectorial bilevel optimization problems. The upper level is a scalar optimization problem to be solved by the leader, and the lower level is a multiobjective optimization problem to be solved by several followers acting in a cooperative way inside the greatest coalition, so choosing among Pareto solutions. In the so-called “optimistic problem”, the followers choose among their best responses (i.e. Pareto solutions) one which is the most favorable for the leader. The opposite is the “pessimistic problem”, when there is no cooperation between the leader and the followers, and the followers choice among their best responses may be the worst for the leader. The paper presents a general method which allows, under certain mild hypotheses, to transform a semivectorial bilevel problem into an ordinary bilevel optimization. Some applications are given.
MSC: 49J20, 49J27, 90C29, 90C48
keywords: Multiobjective optimization, bilevel optimization, semivectorial bilevel optimization problem
DOI 10.56082/annalsarscimath.2020.1-2.344
†henribonnel@gmail.com Curtin University, School of Electrical Engineering, Computing and Mathematical Sciences, Mathematics and Statistics, Kent St, Bentley WA 6102, Australia.
‡ The author is grateful to the anonymous referee for his comments and for his careful reading of the manuscript.
PUBLISHED in Annals Academy of Romanian Scientists Series on Mathematics and Its Application, Volume 12 no 1-2, 2020
