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

Zolezzi, T.

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

Keywords:

variational convergence; well-posedness; stability analysis; abstract minimum problems; ordinary differential inclusions

Citations:

Zbl 0595.00017; Zbl 0169.139