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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.

MSC:
90C31Sensitivity, stability, parametric optimization
49J27Optimal control problems in abstract spaces (existence)
90C25Convex programming
90C48Programming in abstract spaces
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