Publication
Title
High-order methods beyond the classical complexity bounds : inexact high-order proximal-point methods
Author
Abstract
We introduce a Bi-level OPTimization (BiOPT) framework for minimizing the sum of two convex functions, where one of them is smooth enough. The BiOPT framework offers three levels of freedom: (i) choosing the order p of the proximal term; (ii) designing an inexact pth-order proximal-point method in the upper level; (iii) solving the auxiliary problem with a lower-level non-Euclidean method in the lower level. We here regularize the objective by a th-order proximal term (for arbitrary integer ) and then develop the generic inexact high-order proximal-point scheme and its acceleration using the standard estimating sequence technique at the upper level. This follows at the lower level with solving the corresponding pth-order proximal auxiliary problem inexactly either by one iteration of the pth-order tensor method or by a lower-order non-Euclidean composite gradient scheme. Ultimately, it is shown that applying the accelerated inexact pth-order proximal-point method at the upper level and handling the auxiliary problem by the non-Euclidean composite gradient scheme lead to a 2q-order method with the convergence rate (for and the iteration counter k), which can result to a superfast method for some specific class of problems.
Language
English
Source (journal)
Mathematical programming. - Amsterdam, 1971, currens
Publication
Heidelberg : Springer heidelberg , 2024
ISSN
0025-5610 [print]
1436-4646 [online]
DOI
10.1007/S10107-023-02041-4
Volume/pages
(2024) , p. 1-43
ISI
001136171900002
Full text (Publisher's DOI)
Full text (open access)
UAntwerpen
Faculty/Department
Research group
Project info
Taming Nonconvexity in Structured Low-Rank Optimization.
Evaluation complexity of non-Euclidean optimization methods.
Publication type
Subject
Affiliation
Publications with a UAntwerp address
External links
Web of Science
Record
Identifier
Creation 01.02.2024
Last edited 06.02.2024
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