Nonemptiness and Compactness of Solution Sets to Weakly Homogeneous Generalized Variational Inequalities

In this paper, we deal with the weakly homogeneous generalized variational inequality, which provides a unified setting for several special variational inequalities and complementarity problems studied in recent years. By exploiting weakly homogeneous structures of involved map pairs and using degre...

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Bibliographic Details
Published in:Journal of optimization theory and applications 2021-06, Vol.189 (3), p.919-937
Main Authors: Zheng, Meng-Meng, Huang, Zheng-Hai, Bai, Xue-Li
Format: Article
Language:English
Subjects:
Applications of Mathematics
Calculus of Variations and Optimal Control
Optimization
Engineering
Estimates
Existence theorems
Homogeneous structure
Inequalities
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Theory of Computation
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Summary:In this paper, we deal with the weakly homogeneous generalized variational inequality, which provides a unified setting for several special variational inequalities and complementarity problems studied in recent years. By exploiting weakly homogeneous structures of involved map pairs and using degree theory, we establish a result which demonstrates the connection between weakly homogeneous generalized variational inequalities and weakly homogeneous generalized complementarity problems. Subsequently, we obtain a result on the nonemptiness and compactness of solution sets to weakly homogeneous generalized variational inequalities by utilizing Harker–Pang-type condition, which can lead to a Hartman–Stampacchia-type existence theorem. Last, we give several copositivity results for weakly homogeneous generalized variational inequalities, which can reduce to some existing ones.
ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-021-01866-3