Name
Title | ||
|---|---|---|
Variable Metric Forward---Backward Algorithm for Minimizing the Sum of a Differentiable Function and a Convex Function |
Abstract | ||
|---|---|---|
We consider the minimization of a function G defined on ${ \mathbb{R} } ^{N}$ , which is the sum of a (not necessarily convex) differentiable function and a (not necessarily differentiable) convex function. Moreover, we assume that G satisfies the Kurdyka--- ojasiewicz property. Such a problem can be solved with the Forward---Backward algorithm. However, the latter algorithm may suffer from slow convergence. We propose an acceleration strategy based on the use of variable metrics and of the Majorize---Minimize principle. We give conditions under which the sequence generated by the resulting Variable Metric Forward---Backward algorithm converges to a critical point of G . Numerical results illustrate the performance of the proposed algorithm in an image reconstruction application. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1007/s10957-013-0465-7 | Journal of Optimization Theory and Applications |
Keywords | Field | DocType |
proximity operator,nonconvex optimization,image reconstruction,nonsmooth optimization,majorize---minimize algorithms,forward---backward algorithm | Convergence (routing),Iterative reconstruction,Discrete mathematics,Mathematical optimization,Forward–backward algorithm,Mathematical analysis,Regular polygon,Convex function,Differentiable function,Minification,Acceleration,Mathematics | Journal |
Volume | Issue | ISSN |
162 | 1 | 1573-2878 |
Citations | PageRank | References |
46 | 1.50 | 19 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Emilie Chouzenoux | 1 | 202 | 26.37 |
| Jean-Christophe Pesquet | 2 | 560 | 46.10 |
| Audrey Repetti | 3 | 76 | 6.84 |