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Résumé
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 p-th order Taylor model and show
that the algorithm can produce an (epsilon,delta)-approximate q-th-order
stationary point at most O(epsilon^{-(p+1)/(p-q+1)}) evaluations of the
objective function and its first p derivatives (whenever they exist). Our
model 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 \ell_2-\ell_a norm with a in (0,1). The
new result shows that the partially-separable structure and non-Lipschitzian
group sparsity terms in the objective function may not affect the worst-case
evaluation complexity order.
convexly-constrained optimization involving non-Lipschitzian group sparsity
terms in a nonconvex objective function. We propose a partially separable
adaptive regularization algorithm using a p-th order Taylor model and show
that the algorithm can produce an (epsilon,delta)-approximate q-th-order
stationary point at most O(epsilon^{-(p+1)/(p-q+1)}) evaluations of the
objective function and its first p derivatives (whenever they exist). Our
model 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 \ell_2-\ell_a norm with a in (0,1). The
new result shows that the partially-separable structure and non-Lipschitzian
group sparsity terms in the objective function may not affect the worst-case
evaluation complexity order.
langue originale | Anglais |
---|---|
Pages (de - à) | 1-27 |
Nombre de pages | 27 |
journal | Mathematical Programming |
Volume | 1902.10767 |
Les DOIs | |
Etat de la publication | Accepté/sous presse - 1 janv. 2020 |
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Projets
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Complexity in nonlinear optimization
TOINT, P., Gould, N. I. M. & Cartis, C.
1/11/08 → …
Projet: Recherche
Activités
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Recent results in worst-case evaluation complexity for smooth and non-smooth, exact and inexact, nonconvex optimization
Philippe TOINT (Orateur)
8 mai 2020Activité: Types de discours ou de présentation › Discours invité
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Departement of Applied Mathematics, Polytechnic University of Hong Kong
Philippe Toint (Chercheur visiteur)
15 nov. 2018 → 15 déc. 2018Activité: Types de Visite d'une organisation externe › Visite à une institution académique externe