@article{88de5c3caf9644ec88443f79f04f2691,
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 separableconvexly-constrained optimization involving non-Lipschitzian group sparsityterms in a nonconvex objective function. We propose a partially separableadaptive regularization algorithm using a p-th order Taylor model and showthat the algorithm can produce an (epsilon,delta)-approximate q-th-orderstationary point at most O(epsilon^{-(p+1)/(p-q+1)}) evaluations of theobjective function and its first p derivatives (whenever they exist). Ourmodel uses the underlying rotational symmetry of the Euclidean norm functionto build a Lipschitzian approximation for the non-Lipschitzian group sparsityterms, which are defined by the group \ell_2-\ell_a norm with a in (0,1). Thenew result shows that the partially-separable structure and non-Lipschitziangroup sparsity terms in the objective function may not affect the worst-caseevaluation complexity order.",
keywords = "complexity theory, nonlinear optimization, non-Lipschitz functions, partially-separable problems, group sparsity, isotropic model, nonlinear optimization, non-Lipschitz functions, partially-separable problems, group sparsity, isotropic model",
author = "Xiaojun Chen and Philippe Toint",
note = "Funding Information: Xiaojun Chen would like to thank Hong Kong Research Grant Council for Grant PolyU153001/18P. Philippe Toint would like to thank the Hong Kong Polytechnic University for its support while this research was being conducted. We would like to thank the editor and two referees for their helpful comments. Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature and Mathematical Optimization Society.",
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",
}