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

Meng-Meng Zheng (), Zheng-Hai Huang () and Xue-Li Bai ()
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Meng-Meng Zheng: Tianjin University
Zheng-Hai Huang: Tianjin University
Xue-Li Bai: South China Normal University

Journal of Optimization Theory and Applications, 2021, vol. 189, issue 3, No 11, 919-937

Abstract: Abstract 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.

Keywords: Weakly homogeneous map; Generalized variational inequality; Harker–Pang-type condition; Copositivity; Hartman–Stampacchia-type theorem; 65K10; 90C33 (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1007/s10957-021-01866-3

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