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Well-posedness and stability analysis in optimization. (English) Zbl 0624.49011

Fermat days 85: Mathematics for optimization, Toulouse/France 1985, North-Holland Math. Stud. 129, 305-320 (1986).
[For the entire collection see Zbl 0595.00017.]
Some results are described about well-posedness and stability analysis in abstract minimum problems and optimal control of ordinary differential inclusions. These results may be formulated in an abstract form which shows connection between stability analysis and variational extensions of minimum problems in the sense of A. D. Ioffe and V. M. Tikhomirov [Trans. Mosc. Math. Soc. 18, 207-273 (1968); translation from Tr. Mosk. Mat. O.-va 18, 187-246 (1968; Zbl 0169.139)]. Hadamard and Tikhonov well-posedness of convex minimum problems in Banach spaces is also considered.
Reviewer: A.Shapiro

MSC:

49K40 Sensitivity, stability, well-posedness
34A60 Ordinary differential inclusions
49K27 Optimality conditions for problems in abstract spaces
49J45 Methods involving semicontinuity and convergence; relaxation
54A20 Convergence in general topology (sequences, filters, limits, convergence spaces, nets, etc.)
93B05 Controllability
90C25 Convex programming