On the stability of closed-convex-valued mappings and the associated boundaries |
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Authors: | MA Goberna MI Todorov |
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Institution: | a Department of Statistics and Operations Research, Alicante University, Ctra. San Vicente de Raspeig s/n, 03071 Alicante, Spain b Department of Physics and Mathematics, UDLA, 72820 San Andrés Cholula, Puebla, Mexico |
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Abstract: | This paper deals with the stability properties of those set-valued mappings from locally metrizable spaces to Euclidean spaces for which the images are the convex hull of their boundaries (i.e., they are closed convex sets not containing a halfspace). Examples of this class of mappings are the feasible set and the optimal set of convex optimization problems, and the solution set of convex systems, when the data are subject to perturbations. More in detail, we associate with the given set-valued mapping its corresponding boundary mapping and we analyze the transmission of the stability properties (lower and upper semicontinuity, continuity and closedness) from the given mapping to its boundary and vice versa. |
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Keywords: | Closed-convex-valued mappings Boundary mappings Stability theory Upper and lower semicontinuity of mappings Convex optimization |
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