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Unified approaches to well-posedness with some applications. (English) Zbl 1080.49021

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.

MSC:

49K40 Sensitivity, stability, well-posedness
90C31 Sensitivity, stability, parametric optimization

Citations:

Zbl 0960.90079
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