WHEN SEMIVECTORIAL BILEVEL OPTIMIZATION REDUCES TO ORDINARY BILEVEL OPTIMIZATION

Q4 Mathematics

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Pub Date : 2020-01-01 DOI:10.56082/annalsarscimath.2020.1-2.344

H. Bonnel

引用次数: 0

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.

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当半矢量双层优化化为普通双层优化时

本文研究半向量双层优化问题。上层是由领导者解决的标量优化问题，下层是由最大联盟内的多个follower以合作方式解决的多目标优化问题，即在Pareto解中进行选择。在所谓的“乐观问题”中，追随者从他们的最佳反应(即帕累托解决方案)中选择对领导者最有利的一个。相反的是“悲观问题”，当领导者和追随者之间没有合作时，追随者在他们的最佳反应中做出的选择可能对领导者来说是最坏的。本文提出了一种一般方法，在一定的温和假设下，可以将半向量双层问题转化为普通双层优化问题。给出了一些应用。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of the Academy of Romanian Scientists: Series on Mathematics and its Applications Mathematics-Mathematics (all)

CiteScore

0.60

自引率

0.00%

发文量

审稿时长

25 weeks

期刊介绍： The journal Mathematics and Its Applications is part of the Annals of the Academy of Romanian Scientists (ARS), in which several series are published. Although the Academy is almost one century old, due to the historical conditions after WW2 in Eastern Europe, it is just starting with 2006 that the Annals are published. The Editor-in-Chief of the Annals is the President of ARS, Prof. Dr. V. Candea and Academician A.E. Sandulescu (†) is his deputy for this domain. Mathematics and Its Applications invites publication of contributed papers, short notes, survey articles and reviews, with a novel and correct content, in any area of mathematics and its applications. Short notes are published with priority on the recommendation of one of the members of the Editorial Board and should be 3-6 pages long. They may not include proofs, but supplementary materials supporting all the statements are required and will be archivated. The authors are encouraged to publish the extended version of the short note, elsewhere. All received articles will be submitted to a blind peer review process. Mathematics and Its Applications has an Open Access policy: all content is freely available without charge to the user or his/her institution. Users are allowed to read, download, copy, distribute, print, search, or link to the full texts of the articles in this journal without asking prior permission from the publisher or the author. No submission or processing fees are required. Targeted topics include : Ordinary and partial differential equations Optimization, optimal control and design Numerical Analysis and scientific computing Algebraic, topological and differential structures Probability and statistics Algebraic and differential geometry Mathematical modelling in mechanics and engineering sciences Mathematical economy and game theory Mathematical physics and applications.