Universal gradient methods for convex optimization problems

  title={Universal gradient methods for convex optimization problems},
  author={Yurii Nesterov},
  journal={Math. Program.},
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. The 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… CONTINUE READING
Highly Influential
This paper has highly influenced 13 other papers. REVIEW HIGHLY INFLUENTIAL CITATIONS
44 Citations
12 References
Similar Papers


Publications citing this paper.
Showing 1-10 of 44 extracted citations


Publications referenced by this paper.
Showing 1-10 of 12 references

Problem complexity and method efficiency in optimization

  • A. Nemirovsky, D. Yudin
  • 1983
Highly Influential
4 Excerpts

Nesterov . “ Smooth minimization of nonsmooth functions ”

  • Yu.
  • Mathematical Programming ( A )
  • 2005

Nesterov . New variants of bundle methods

  • C. Lemarechal, A. Nemirovskii, Yu.
  • Mathematical Programming
  • 1995

Nesterov . First - order methods of smooth convex optimization with inexact oracle

  • Yu.
  • Modern Mathematical Methods in Optimization
  • 1993

Similar Papers

Loading similar papers…