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3447. Avoiding strict saddle points of nonconvex regularized problems
Invited abstract in session TD-41: Lower-order composite optimization problems, stream Nonsmooth Optimization.
Tuesday, 14:30-16:00Room: 97 (building: 306)
Authors (first author is the speaker)
| 1. | Hao Wang
|
| Information Science and Technology, ShanghaiTech University |
Abstract
In this paper, we consider a class of non-convex and non-smooth sparse optimization problems, which encompass most existing nonconvex sparsity-inducing terms. These problems, moreover, are probably non-lipschitz around sparse solutions. We propose an damped iterative reweighted l1 algorithm to solve these problems. The algorithm is guaranteed to converge only to local minimizers when randomly initialized. By deriving a second-order sufficient optimal condition under the non-degenerate assumption, we show that the strict saddle property is generic on these sparse optimization problems.
Keywords
- Non-smooth Optimization
- Continuous Optimization
- Mathematical Programming
Status: accepted
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