Well-posedness of mixed variational inequalities, inclusion problems and fixed point problems

Authors:
Ya-Ping Fang;Nan-Jing Huang;Jen-Chih Yao
Affiliations:
Department of Mathematics, Sichuan University, Chengdu, Sichuan, People's Republic of China 610064;Department of Mathematics, Sichuan University, Chengdu, Sichuan, People's Republic of China 610064;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan, Republic of China
Venue:
Journal of Global Optimization
Year:
2008

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Abstract

We generalize the concept of well-posedness to a mixed variational inequality and give some characterizations of its well-posedness. Under suitable conditions, we prove that the well-posedness of a mixed variational inequality is equivalent to the well-posedness of a corresponding inclusion problem. We also discuss the relations between the well- posedness of a mixed variational inequality and the well-posedness of a fixed point problem. Finally, we derive some conditions under which a mixed variational inequality is well-posed.