@article{7f5f7a6337a6416b8d3c00afbcd5309c,
title = "High-Order Evaluation Complexity for Convexly-Constrained Optimization with Non-Lipschitzian Group Sparsity Terms",
abstract = "This paper studies high-order evaluation complexity for partially separable convexly-constrained optimization involving non-Lipschitzian group sparsity terms in a nonconvex objective function. We propose a partially separable adaptive regularization algorithm using a pth order Taylor model and show that the algorithm needs at most O(ϵ- ( p + 1 ) / ( p - q + 1 )) evaluations of the objective function and its first p derivatives (whenever they exist) to produce an (ϵ, δ) -approximate qth-order stationary point. Our algorithm uses the underlying rotational symmetry of the Euclidean norm function to build a Lipschitzian approximation for the non-Lipschitzian group sparsity terms, which are defined by the group ℓ2–ℓa norm with a∈ (0 , 1). The new result shows that the partially-separable structure and non-Lipschitzian group sparsity terms in the objective function do not affect the worst-case evaluation complexity order.",
keywords = "Complexity theory, Group sparsity, Isotropic model, Non-Lipschitz functions, Nonlinear optimization, Partially-separable problems",
author = "X. Chen and Toint, {Ph L.}",
year = "2021",
month = may,
doi = "10.1007/s10107-020-01470-9",
language = "English",
volume = "187",
pages = "47--78",
journal = "Mathematical Programming",
issn = "0025-5610",
publisher = "Springer-Verlag GmbH and Co. KG",
number = "1-2",
}