Preservation of convergence of convex sets and functions in finite dimensions
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- by L. McLinden and Roy C. Bergstrom PDF
- Trans. Amer. Math. Soc. 268 (1981), 127-142 Request permission
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.References
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Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 268 (1981), 127-142
- MSC: Primary 26B25; Secondary 65K10
- DOI: https://doi.org/10.1090/S0002-9947-1981-0628449-5
- MathSciNet review: 628449