Nesterov, Yurii
[UCL]
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.
- Babonneau Frédéric, Nesterov Yurii, Vial Jean-Philippe, Design and Operations of Gas Transmission Networks, 10.1287/opre.1110.1001
- Beck Amir, Teboulle Marc, A Fast Iterative Shrinkage-Thresholding Algorithm for Linear Inverse Problems, 10.1137/080716542
- Devolder Olivier, Glineur François, Nesterov Yurii, First-order methods of smooth convex optimization with inexact oracle, 10.1007/s10107-013-0677-5
- Elster, K.-H. (ed.): Modern Mathematical Methods in Optimization. Academie Verlag, Berlin (1993)
- Lan Guanghui, Bundle-level type methods uniformly optimal for smooth and nonsmooth convex optimization, 10.1007/s10107-013-0737-x
- Lemaréchal Claude, Nemirovskii Arkadii, Nesterov Yurii, New variants of bundle methods, 10.1007/bf01585555
- Nemirovskii, A., Nesterov, Yu.: Optimal methods for smooth convex optimization. Zh. Vychisl. Mat. i Mat. Fiz. 25(3), 356–369 (1985). in Russian
- Nemirovsky, A., Yudin, D.: Problem Complexity and Method Efficiency in Optimization. Wiley, New York (1983)
- Nesterov Yurii, Introductory Lectures on Convex Optimization, ISBN:9781461346913, 10.1007/978-1-4419-8853-9
- Nesterov Yu., Smooth minimization of non-smooth functions, 10.1007/s10107-004-0552-5
- Nesterov Yu., Gradient methods for minimizing composite functions, 10.1007/s10107-012-0629-5
- Nesterov Yurii, Primal-dual subgradient methods for convex problems, 10.1007/s10107-007-0149-x
Bibliographic reference |
Nesterov, Yurii. Universal gradient methods for convex optimization problems. In: Mathematical Programming, Vol. 152, no.1, p. 381-404 (August 2015) |
Permanent URL |
http://hdl.handle.net/2078.1/181314 |