Metrically well-set minimization problems. (English) Zbl 0762.90073

Summary: A concept of well-posedness, or more exactly of stability in a metric sense, is introduced for minimization problems on metric spaces generalizing the notion due to Tykhonov to situations in which there is no uniqueness of solutions. It is compared with other concepts, in particular to a variant of the notion after Hadamard reformulated via a metric semicontinuity approach. Concrete criteria of well-posedness are presented, e.g., for convex minimization problems.


90C31 Sensitivity, stability, parametric optimization
49J27 Existence theories for problems in abstract spaces
90C25 Convex programming
90C48 Programming in abstract spaces
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