期刊
MATHEMATICAL PROGRAMMING
卷 152, 期 1-2, 页码 381-404出版社
SPRINGER HEIDELBERG
DOI: 10.1007/s10107-014-0790-0
关键词
Convex optimization; Black-box methods; Complexity bounds; Optimal methods; Weakly smooth functions
类别
资金
- grant Action de recherche concerte from the Direction de la recherche scientifique - Communaute francaise de Belgique [ARC 04/09-315]
- Laboratory of Structural Methods of Data Analysis in Predictive Modelling, through RF [11.G34.31.0073]
- RFBR [13-01-12007 ofi_m, 14-01-00722-a]
In this paper, we present new methods for black-box convex minimization. They do not need to know in advance the actual level of smoothness of the objective function. Their only essential input parameter is the required accuracy of the solution. At the same time, for each particular problem class they automatically ensure the best possible rate of convergence. We confirm our theoretical results by encouraging numerical experiments, which demonstrate that the fast rate of convergence, typical for the smooth optimization problems, sometimes can be achieved even on nonsmooth problem instances.
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