LIU Dan-yang, JIANG Ya. Scalarization of Mixed Vector Variational Inequalities and Error Bounds of Gap Functions[J]. Applied Mathematics and Mechanics, 2017, 38(6): 715-726. doi: 10.21656/1000-0887.370292
Citation: LIU Dan-yang, JIANG Ya. Scalarization of Mixed Vector Variational Inequalities and Error Bounds of Gap Functions[J]. Applied Mathematics and Mechanics, 2017, 38(6): 715-726. doi: 10.21656/1000-0887.370292

Scalarization of Mixed Vector Variational Inequalities and Error Bounds of Gap Functions

doi: 10.21656/1000-0887.370292
Funds:  The National Natural Science Foundation of China(11371015)
  • Received Date: 2016-09-23
  • Rev Recd Date: 2017-05-10
  • Publish Date: 2017-06-15
  • The Konnov scalarization method for variational inequality problems was used to further generalize the classical strongly variational inequalities (SVIs) and the classical weakly variational inequalities (WVIs). The strongly generalized mixed vector variational inequalities (SGMVVIs) and the weakly generalized mixed vector variational inequalities (WGMVVIs) were studied based on setvalued mappings in view of their gap functions. Under proper conditions, the relationship between the gap function of the strongly generalized mixed setvalued variational inequality (SGMVI) and that of the SGMVVI, and the relationship between the gap functions of the WGMVVI and the SGMVI, were discussed. At last, the global error bounds of the gap functions were obtained.
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