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237. A Proximal Variable Smoothing for Nonsmooth Minimization of the Sum of Three Functions Including Weakly Convex Composite Function
Invited abstract in session MD-6: Smoothing techniques for nonsmooth optimization, stream Nonsmooth and nonconvex optimization.
Monday, 16:30-18:30Room: B100/7013
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
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