一类非单调互补问题的Canonical对偶问题研究

doi:10.12005/orms.2021.0001

运筹与管理 ›› 2021, Vol. 30 ›› Issue (1): 1-5.DOI: 10.12005/orms.2021.0001

• 理论分析与方法探讨 • 下一篇

一类非单调互补问题的Canonical对偶问题研究

刘国山¹, 丁冰洁², 刁海璨³

中国人民大学商学院,北京 100872

收稿日期:2020-05-06 出版日期:2021-01-25
作者简介:刘国山(1962-),男,吉林人,教授,博士。研究方向:双层规划、量化交易等相关算法研究;丁冰洁(1991-),女,安徽人,博士。研究方向:运筹优化、博弈;刁海璨(1995-),女,山东人,博士。研究方向:双层规划、量化交易。
基金资助:
中国人民大学2019年度研究生科学研究基金资助项目(19XNH089)

Canonical Duality for a Class of Nonmonotone Complementarity Problems

LIU Guo-shan¹, DING Bing-jie², DIAO Hai-can³

School of Business, Renmin University of China, Beijing 100872, China

Received:2020-05-06 Online:2021-01-25

摘要/Abstract

摘要： 对于一类具有广泛应用背景的非单调互补问题,我们构建了这类问题的Canonical对偶问题。其对偶问题可以写成和原问题类似的互补问题。我们给出了对偶问题和原问题解之间的对偶关系,并且将对偶问题转化成一个一维优化问题,这不但可以方便的求解这类问题,也为研究这类问题性质提供了一个非常直观的研究工具。最后,本文给出了几个算例来演示对偶问题的性质。

关键词: 互补问题, 非线性优化, 变分不等式, Canonical对偶

Abstract: We construct a canonical dual problem for a class of non-monotonic complementary problems with a wide range of applications. The dual problems can be written as complementary problems with the same structure to the original problem. We discuss the relationship between the solution of the dual problem and that of the original problem. Then we transform the dual problem into a one-dimensional optimization one, which not only can be easily solved, but also provides a very intuitive research tool for studying the properties of this kind of problem. Finally, we give a few examples to demonstrate the properties of the dual problem.

Key words: complementarity problem, nonlinear programming, variational inequality, canonical duality

中图分类号:

刘国山, 丁冰洁, 刁海璨. 一类非单调互补问题的Canonical对偶问题研究[J]. 运筹与管理, 2021, 30(1): 1-5.

LIU Guo-shan, DING Bing-jie, DIAO Hai-can. Canonical Duality for a Class of Nonmonotone Complementarity Problems[J]. Operations Research and Management Science, 2021, 30(1): 1-5.

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一类非单调互补问题的Canonical对偶问题研究

Canonical Duality for a Class of Nonmonotone Complementarity Problems

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