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.
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Yang, H., Yu, J. Unified Approaches to Well-Posedness with Some Applications. J Glob Optim 31, 371–381 (2005). https://doi.org/10.1007/s10898-004-4275-1
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DOI: https://doi.org/10.1007/s10898-004-4275-1