Local Minimizers of Nonconvex Functions in Banach Spaces via Moreau Envelopes
arxiv(2023)
Abstract
This paper investigates the preservation of local minimizers and strong
minimizers of extended-real-valued lower semicontinuous functions under taking
their Moreau envelopes. We address a general setting of Banach spaces, while
all the obtained results are new even for functions in finite dimensions. Our
main motivation came from applications to numerical methods in nonsmooth
optimization dealing with broad classes of nondifferentiable and nonconvex
functions. The paper also formulates and discusses some open questions stemming
from this study.
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