On local coincidence of a convex set and its tangent cone
- Authors: Meng, Kaiwen , Roshchina, Vera , Yang, Xiaoqi
- Date: 2015
- Type: Text , Journal article
- Relation: Journal of Optimization Theory and Applications Vol. 164, no. 1 (2015), p. 123-137
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- Description: In this paper, we introduce the exact tangent approximation property for a convex set and provide its characterizations, including the nonzero extent of a convex set. We obtain necessary and sufficient conditions for the closedness of the positive hull of a convex set via a limit set defined by truncated upper level sets of the gauge function. We also apply the exact tangent approximation property to study the existence of a global error bound for a proper, lower semicontinuous and positively homogeneous function.
Outer limits of subdifferentials for min–max type functions
- Authors: Eberhard, Andrew , Roshchina, Vera , Sang, Tian
- Date: 2019
- Type: Text , Journal article
- Relation: Optimization Vol. 68, no. 7 (2019), p. 1391-1409
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- Description: We generalize the outer subdifferential construction suggested by Cánovas, Henrion, López and Parra for max type functions to pointwise minima of regular Lipschitz functions. We also answer an open question about the relation between the outer subdifferential of the support of a regular function and the end set of its subdifferential posed by Li, Meng and Yang.