单调混合变分不等式解集性质
Properties of Solution Set for Monotonic Mixed Variational Inequalities
摘要: 本文研究了单调混合变分不等式的解集性质。利用f投影算子我们知道一点是单调混合变分不等式的解当且仅当为f投影的不动点。结合这个结论我们得到了关于单调混合变分不等式解集的一些性质。
Abstract:
This article investigates the properties of the solution set for monotonic mixed variational ine-qualities. Using the f-projection operator, we know that a point is a solution for monotonic mixed variational inequalities if and only if it is a fixed point for the f-projection. Based on this conclusion, we obtain some properties about the solution set for monotonic mixed variational inequalities.
参考文献
|
[1]
|
周晶. 随机交通均衡配流模型及其等价的变分不等式问题[J]. 系统科学与数学, 2003, 23(1): 120-127.
|
|
[2]
|
李润梅, 汤淑明, 王飞跃. 动态用户最优的变分不等式分配模型研究综述[J]. 交通运输系统工程与信息, 2006, 6(2): 8.
|
|
[3]
|
丁方允, 张欣, 丁睿. 摩擦问题中的边界混合变分不等式[J]. 应用数学和力学, 1999, 20(2): 201-210.
|
|
[4]
|
郇宁, 姚恩建, 杨扬, 等. 电动汽车混入条件下随机动态用户均衡分配模型[J]. 交通运输工程学报, 2019, 19(5): 150-161.
|
|
[5]
|
Wu, K.Q. and Huang, N.J. (2006) The Generalised f-Projection Operator with an Application. Bulletin of the Australian Mathematical Society, 73, 307-317. [Google Scholar] [CrossRef]
|
|
[6]
|
Wu, K.Q. and Huang, N.J. (2007) Properties of the Generalized-Projection Operator and Its Applications in Banach Spaces. Computers & Mathematics with Applications, 54, 399-406. [Google Scholar] [CrossRef]
|
|
[7]
|
Wu, K.Q. and Huang, N.J. (2009) The Generalized F-Projection Operator and Set-Valued Variational Inequalities in Banach Spaces. Nonlinear Analysis, 71, 2481-2490. [Google Scholar] [CrossRef]
|
|
[8]
|
Lescarret, C. (1965) Cas d’addition des applications monotones maximales dans un espace de Hilbert. Comptes rendus hebdomadaires des séances de l’Académie des sciences. 261, 1160-1163.
|
|
[9]
|
Browder, F.E. (1966) On the Unification of the Calculus of Variations and the Theory of Monotone Nonlinear Operators in Banach Spaces. Proceedings of the National Academy of Sciences of the United States of America, 56, 419-425. [Google Scholar] [CrossRef] [PubMed]
|