EURO-Online login
- New to EURO? Create an account
- I forgot my username and/or my password.
- Help with cookies
(important for IE8 users)
237. A Proximal Variable Smoothing for Nonsmooth Minimization of the Sum of Three Functions Including Weakly Convex Composite Function
Invited abstract in session Smoothing techniques for nonsmooth optimization, stream Nonsmooth and nonconvex optimization.
Authors (first author is the speaker)
| 1. | Keita Kume
|
| Department of Information and Communications Engineering, Institute of Science Tokyo | |
| 2. | Isao Yamada
|
| Department of Information and Communications Engineering, Institute of Science Tokyo |
Abstract
We propose a proximal variable smoothing algorithm for a nonsmooth optimization problem whose cost function is the sum of three functions including a weakly convex composite function. The proposed algorithm has a single-loop structure inspired by a proximal gradient-type method. More precisely, the proposed algorithm consists of two steps: (i) a gradient descent of a time-varying smoothed surrogate function designed partially with the Moreau envelope of the weakly convex function; (ii) an application of the proximity operator of the remaining function not covered by the smoothed surrogate function. We also present a convergence analysis of the proposed algorithm by exploiting a novel asymptotic approximation of a gradient-mapping-type stationarity measure.
Keywords
- Optimal control and applications
- Non-smooth optimization
- First-order optimization
Status: accepted
Back to the list of papers