## Quantitative stability of variational systems. I: The epigraphical distance.(English)Zbl 0753.49007

A notion of distance between the elements of a variational system (i.e. a parametrized family of optimization problems) is proposed in order to obtain quantitative information about continuity properties of the minimum value function, or of the set of optimal solutions. The authors define a family $$\{hausd_ \rho; \rho\geq 0\}$$ of pseudo-distances between extended real-valued functions, defined on a normed linear space, to which they refer as epi-distance, providing a cirterion for its evaluation in practical situations. They make a comparison between epi- distance and other notions of distance. They investigate the relationship between the epi-distance topology and the topology of epi-convergence (also known in the literature as $$\Gamma$$-convergence) and they consider the related convergence notion for monotone operators.
Reviewer: A.Leaci (Lecce)

### MSC:

 49J45 Methods involving semicontinuity and convergence; relaxation 49K40 Sensitivity, stability, well-posedness
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