Preservation of Convergence of Convex Sets and Functions in Finite Dimensions
Authors:
- L. McLindenLML. McLinden
- Roy C. BergstromRBRoy C. Bergstrom
- 1 November 1981
- journal article
- Published by JSTOR in Transactions of the American Mathematical Society
- Vol. 268 (1) , 127-142
Abstract
We study a convergence notion which has particular relevance for convex analysis and lends itself quite naturally to successive approximation schemes in a variety of areas. Motivated particularly by problems in optimization subject to constraints, we develop technical tools necessary for systematic use of this convergence in finite-dimensional settings. Simple conditions are established under which this convergence for sequences of sets, functions and subdifferentials is preserved under various basic operations, including, for example, those of addition and infimal convolution in the case of functions.Keywords
This publication has 10 references indexed in Scilit:
- Successive approximation and linear stability involving convergent sequences of optimization problemsJournal of Approximation Theory, 1982
- Familles d'opérateurs maximaux monotones et mesurabilitéAnnali di Matematica Pura ed Applicata (1923 -), 1979
- On the Convergence of Sequences of Convex Sets in Finite DimensionsSIAM Review, 1979
- On the relations between two types of convergence for convex functionsJournal of Mathematical Analysis and Applications, 1977
- On the continuity of the Young-Fenchel transformJournal of Mathematical Analysis and Applications, 1971
- Convex Analysis1970
- Convergence of convex sets and of solutions of variational inequalitiesAdvances in Mathematics, 1969
- Continuity of Some Convex-Cone-Valued MappingsProceedings of the American Mathematical Society, 1967
- Convergence of Sequences of Convex Sets, Cones and Functions. IITransactions of the American Mathematical Society, 1966
- Convergence of sequences of convex sets, cones and functionsBulletin of the American Mathematical Society, 1964