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Operations Research Transactions >

2025 , Vol. 29 >Issue 2: 44 - 57

DOI: https://doi.org/10.15960/j.cnki.issn.1007-6093.2025.02.003

Research Article

Gap functions and error bounds for generalized mixed quasi-variational inequalities

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  • 1. School of Mathematics and Statistics, Fujian Normal University, Fuzhou 350117, Fujian, China

Received date: 2022-03-15

  Online published: 2025-06-12

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, 2025, All rights reserved. Unauthorized reproduction is prohibited.
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Abstract

A generalized mixed quasi-variational inequality (GMQVI) is a generalization of the variational inequality. Variational inequalities and their generalization are widely used, for instance, economics, transportation and optimal control. Based on the intrinsic properties of the generalized projection operator, under certain assumptions of monotonicity and compactness, this paper gives the regularized gap function for generalized mixed quasi-variational inequality problems in reflexive Banach spaces, which in turn induces the D-gap function for GMQVI by the difference of two regularized gap functions. And using these gap functions, the local error bound described by the regularized gap function and the global error bound characterized by the D-gap function and the regularization term are obtained.

Key words： generalized mixed quasi-variational inequalities; gap functions; error bounds

Cite this article

Qiao CHEN, Huiling LIN . Gap functions and error bounds for generalized mixed quasi-variational inequalities[J]. Operations Research Transactions, 2025 , 29(2) : 44 -57 . DOI: 10.15960/j.cnki.issn.1007-6093.2025.02.003

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