期刊
SIAM JOURNAL ON OPTIMIZATION
卷 30, 期 4, 页码 2750-2779出版社
SIAM PUBLICATIONS
DOI: 10.1137/19M1259432
关键词
unconstrained minimization; high-order methods; tensor methods; Holder condition; worst-case global complexity bounds
资金
- National Council for Scientific and Technological Development -Brazil [401288/2014-5, 406269/2016-5]
- European Research Council [788368]
In this paper, we study p-order methods for unconstrained minimization of convex functions that are p-times differentiable (p >= 2) with nu-Holder continuous pth derivatives. We propose tensor schemes with and without acceleration. For the schemes without acceleration, we establish iteration complexity bounds of O (epsilon(-1/(p+nu-1))) for reducing the functional residual below a given epsilon is an element of (0, 1). Assuming that nu is known, we obtain an improved complexity bound of O (epsilon(-1/(P+nu))) for the corresponding accelerated scheme. For the case in which nu is unknown, we present a universal accelerated tensor scheme with iteration complexity of O (epsilon(-P/[(P+1)(P+nu-1)])). A lower complexity bound of O (epsilon(-2/[3(P+nu)-2])) is also obtained for this problem class.
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