Generic uniqueness theorems with some applications

We first present a proper condition under which the image of a set-valued mapping becomes a singleton and then obtain several generic uniqueness theorems which can be applied to study the uniqueness of the solutions for nonlinear problems. As applications, we prove that, in the sense of Baire catego...

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Bibliographic Details
Published inJournal of global optimization Vol. 56; no. 2; pp. 713 - 725
Main Authors Peng, Dingtao, Yu, Jian, Xiu, Naihua
Format Journal Article
LanguageEnglish
Published Boston Springer US 01.06.2013
Springer
Springer Nature B.V
Subjects
Categories
Computer Science
Inequalities
Mapping
Mathematical analysis
Mathematics
Mathematics and Statistics
Neighborhoods
Nonlinearity
Operations Research/Decision Theory
Optimization
Real Functions
Saddle points
Studies
Theorems
Uniqueness
Uniqueness theorems
Generic uniqueness
58E35
Set-valued mapping
49K40
Variational inequality problem
Optimization problem
Saddle point
47H04
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Summary:We first present a proper condition under which the image of a set-valued mapping becomes a singleton and then obtain several generic uniqueness theorems which can be applied to study the uniqueness of the solutions for nonlinear problems. As applications, we prove that, in the sense of Baire category, most optimization problems (respectively, saddle point problems and variational inequality problems) have unique solution.
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ISSN:0925-5001
1573-2916
DOI:10.1007/s10898-012-9903-6