×

zbMATH — the first resource for mathematics

The distance to the intersection of two convex sets expressed by the distances to each of them. (English) Zbl 0773.52002
For normed spaces, especially pre-Hilbert spaces, an upper estimate for the distance referred to in the title is given and applied to the intersection of convex set valued maps. Conditions are given which imply that such intersection maps are semicontinuous or Lipschitz.
Reviewer: E.Heil (Darmstadt)

MSC:
52A05 Convex sets without dimension restrictions (aspects of convex geometry)
52A41 Convex functions and convex programs in convex geometry
26B25 Convexity of real functions of several variables, generalizations
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Aubin, Differential inclusions, Grundlehren der mathematischen Wissenschaften 264 (1984)
[2] Dolecki, Semicontinuity in constrained optimization I, II, III, Control Cybernet. 7 pp 1– (1978)
[3] Control Cybernet. II 3 26
[4] Control Cybernet. III 4 68
[5] Rolewicz Dolecki, Metric characterizations of upper semicontinuity, J. Math. Anal. Appl. 69 pp 1– (1979) · Zbl 0414.54012
[6] Hoffmann , A. Weak convex functions multifunctions and optimization 1982 33 36
[7] Kantorovich, Funktionalanalysis in normierten Räumen (1978)
[8] Oniščik, Algebra und Geometrie (1986)
[9] Rolewicz, On paraconvex multifunctions, Operations Res. Verf. 31 pp 539– (1979) · Zbl 0403.49021
[10] Rolewicz, On \(\gamma\)-paraconvex multifunctions, Math. Japon. 24 pp 293– (1979)
[11] Rolewicz, On the intersection of multifunctions, Math. Operationsforschung Statist, Series Optimization 11 pp 3– (1980) · Zbl 0522.54017
[12] Valentine, Konvexe Mengen, Bibliographisches Institut Mannheim (1968)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.