# Gradient methods for minimizing composite functions

@article{Nesterov2013GradientMF,
title={Gradient methods for minimizing composite functions},
author={Y. Nesterov},
journal={Mathematical Programming},
year={2013},
volume={140},
pages={125-161}
}
• Y. Nesterov
• Published 2013
• Mathematics, Computer Science
• Mathematical Programming
In this paper we analyze several new methods for solving optimization problems with the objective function formed as a sum of two terms: one is smooth and given by a black-box oracle, and another is a simple general convex function with known structure. Despite the absence of good properties of the sum, such problems, both in convex and nonconvex cases, can be solved with efficiency typical for the first part of the objective. For convex problems of the above structure, we consider primal and… Expand
920 Citations

#### References

SHOWING 1-10 OF 32 REFERENCES
Gradient Projection for Sparse Reconstruction: Application to Compressed Sensing and Other Inverse Problems
• Computer Science
• IEEE Journal of Selected Topics in Signal Processing
• 2007
Smooth minimization of non-smooth functions
• Y. Nesterov
• Mathematics, Computer Science
• Math. Program.
• 2005
Just relax: convex programming methods for identifying sparse signals in noise
• J. Tropp
• Mathematics, Computer Science
• IEEE Transactions on Information Theory
• 2006
Iterative solution of nonlinear equations in several variables
• Computer Science, Mathematics
• Computer science and applied mathematics
• 1970
Atomic Decomposition by Basis Pursuit
• Mathematics, Computer Science
• SIAM J. Sci. Comput.
• 1998