Yang, Hui; Yu, Jian Unified approaches to well-posedness with some applications. (English) Zbl 1080.49021 J. Glob. Optim. 31, No. 3, 371-381 (2005). Summary: 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 by M. B. Lignola and J. Morgan [J. Global Optim. 16, No. 1, 57–67 (2000; Zbl 0960.90079)] and who 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 well-posedness. Finally, as corollaries, we derive generalized well-posedness and strong well-posedness for these problems. Cited in 1 ReviewCited in 22 Documents MSC: 49K40 Sensitivity, stability, well-posedness 90C31 Sensitivity, stability, parametric optimization Keywords:fixed point; generalized well-posedness; Hadamard well-posedness; Nash equilibrium; optimization problem; strong well-posedness; Tikhonov well-posedness Citations:Zbl 0960.90079 PDF BibTeX XML Cite \textit{H. Yang} and \textit{J. Yu}, J. Glob. Optim. 31, No. 3, 371--381 (2005; Zbl 1080.49021) Full Text: DOI OpenURL References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.