367. NON-EUCLIDEAN PROXIMAL METHODS FOR CONVEX-CONCAVE SADDLE-POINT PROBLEMS
Invited abstract in session TB-6: Advances in nonsmooth optimization, stream Nonsmooth and nonconvex optimization.
Tuesday, 10:30-12:30Room: B100/7013
Authors (first author is the speaker)
| 1. | Eyal Cohen
|
| 2. | Shoham Sabach
|
| Faculty of Industrial Engineering and Management, Technion - Israel Institute of Technology | |
| 3. | Marc Teboulle
|
| School of Mathematical Sciences, Tel Aviv University |
Abstract
Abstract. Motivated by the flexibility of the Proximal Alternating Predictor Corrector (PAPC) algorithm
which can tackle a broad class of structured constrained convex optimization problems via their convex-
concave saddle-point reformulation, in this paper, we extend the scope of the PAPC algorithm to include
non-Euclidean proximal steps. This allows for adapting to the geometry of the problem at hand to
produce simpler computational steps. We prove a sublinear convergence rate of the produced ergodic
sequence, and under additional natural assumptions on the non-Euclidean distances, we also prove that
the algorithm globally converges to a saddle-point. We demonstrate the performance and simplicity of
the proposed algorithm through its application to the multinomial logistic regression problem.
Keywords
- First-order optimization
- Non-smooth optimization
Status: accepted
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