Name
Abstract | ||
|---|---|---|
We propose a unifying algorithm for non-smooth non-convex optimization. The algorithm approximates the objective function by a convex model function and finds an approximate (Bregman) proximal point of the convex model. This approximate minimizer of the model function yields a descent direction, along which the next iterate is found. Complemented with an Armijo-like line search strategy, we obtain a flexible algorithm for which we prove (subsequential) convergence to a stationary point under weak assumptions on the growth of the model function error. Special instances of the algorithm with a Euclidean distance function are, for example, gradient descent, forward–backward splitting, ProxDescent, without the common requirement of a “Lipschitz continuous gradient”. In addition, we consider a broad class of Bregman distance functions (generated by Legendre functions), replacing the Euclidean distance. The algorithm has a wide range of applications including many linear and nonlinear inverse problems in signal/image processing and machine learning. |
Year | DOI | Venue |
|---|---|---|
2017 | 10.1007/s10957-018-01452-0 | Journal of Optimization Theory and Applications |
Keywords | Field | DocType |
Bregman minimization,Legendre function,Model function,Growth function,Non-convex non-smooth,Abstract algorithm,49J52,65K05,65K10,90C26 | Stochastic gradient descent,Gradient descent,Mathematical optimization,Euclidean distance,Proximal Gradient Methods,Algorithm,Descent direction,Stationary point,Bregman divergence,Lipschitz continuity,Mathematics | Journal |
Volume | Issue | ISSN |
abs/1707.02278 | 1 | 0022-3239 |
Citations | PageRank | References |
5 | 0.39 | 16 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Peter Ochs | 1 | 182 | 9.43 |
| Jalal Fadili | 2 | 1184 | 80.08 |
| Thomas Brox | 3 | 7866 | 327.52 |