Generic uniqueness theorems with some applications

Dingtao Peng (), Jian Yu and Naihua Xiu

Journal of Global Optimization, 2013, vol. 56, issue 2, 713-725

Abstract: 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. Copyright Springer Science+Business Media, LLC. 2013

Keywords: Generic uniqueness; Set-valued mapping; Optimization problem; Saddle point; Variational inequality problem; 47H04; 49K40; 58E35 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-9903-6

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