Well-posedness for systems of generalized mixed quasivariational inclusion problems and optimization problems with constraints

Volume 10, Issue 10, pp 5373--5392 http://dx.doi.org/10.22436/jnsa.010.10.23

Publication Date: October 27, 2017 Submission Date: August 07, 2017

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Authors

Lu-Chuan Ceng - Department of Mathematics, Shanghai Normal University, Shanghai 200234, China. Yeong-Cheng Liou - Department of Healthcare Administration and Medical Informatics, Center for Big Data Analytics \(\&\) Intelligent Healthcare, and Research Center of Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung 807, Taiwan. - Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung 807, Taiwan. Jen-Chih Yao - Center for General Education, China Medical University, Taichung, 40402, Taiwan. Yonghong Yao - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China. Ching-Hua Lo - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.

Abstract

In this paper, several metric characterizations of well-posedness for systems of generalized mixed quasivariational inclusion problems and for optimization problems with systems of generalized mixed quasivariational inclusion problems as constraints are given. The equivalence between the well-posedness of systems of generalized mixed quasivariational inclusion problems and the existence of solutions of systems of generalized mixed quasivariational inclusion problems is given under suitable conditions.

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Keywords

• Well-posedness
• metric characterization
• system of generalized mixed quasivariational inclusion problems
• optimization problem with constraint

MSC

•  49J40
•  49J27
•  90C31

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