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Journal of Global Optimization

, Volume 31, Issue 3, pp 371–381 | Cite as

Unified Approaches to Well-Posedness with Some Applications

  • Hui Yang
  • Jian Yu
Article

Abstract

We present unified approaches to Hadamard and Tykhonov well-posedness. As applications, we deduce Tykhonov well- posedness for optimization problems, Nash equilibrium point problems and fixed point problems etc. Especially, by applying such approaches, we deal with the well- posedness as stated in (Lignola and Morgan (2000), Journal of Global Optimization 16, 57–67) in which Lignola and Morgan investigated directly and intensively Tykhonov types of well- posedness for optimization problems with constraints defined by variational inequalities, namely, generalized well- posedness and strong well- posedness. We give some sufficient conditions for Hadamard well- posedness of such problems and deduce relations between Hadamard type and Tykhonov type of well- posedness. Finally, as corollaries, we derive generalized well- posedness and strong well- posedness for these problems.

Keywords

Fixed point Generalized well- posedness Hadamard well- posedness Nash equilibrium Optimization problem Strong well-posedness Tykhonov well- posedness 

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Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of MathematicsGuizhou UniversityGuizhouChina

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