Twice epi-differentiability of extended-real-valued functions with applications in composite optimization
Optimization and Control
2020-04-15 v2
Abstract
The paper is devoted to the study of the twice epi-differentiablity of extended-real-valued functions, with an emphasis on functions satisfying a certain composite representation. This will be conducted under the parabolic regularity, a second-order regularity condition that was recently utilized in [13] for second-order variational analysis of constraint systems. Besides justifying the twice epi-differentiablity of composite functions, we obtain precise formulas for their second subderivatives under the metric subregularity constraint qualification. The latter allows us to derive second-order optimality conditions for a large class of composite optimization problems.
Keywords
Cite
@article{arxiv.1911.05236,
title = {Twice epi-differentiability of extended-real-valued functions with applications in composite optimization},
author = {Ashkan Mohammadi and M. Ebrahim Sarabi},
journal= {arXiv preprint arXiv:1911.05236},
year = {2020}
}