Relaxations for Non-Separable Cardinality/Rank Penalties
| Autor: | Daniele Gerosa, Carl Olsson, Marcus Carlsson |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Rank (linear algebra)
business.industry Stationary point Separable space Discontinuity (linguistics) Singular value Cardinality Optimization and Control (math.OC) Joint probability distribution FOS: Mathematics Applied mathematics Relaxation (approximation) Artificial intelligence business Mathematics - Optimization and Control Mathematics |
| Zdroj: | 2021 IEEE/CVF International Conference on Computer Vision Workshops (ICCVW). |
| Popis: | Rank and cardinality penalties are hard to handle in optimization frameworks due to non-convexity and discontinuity. Strong approximations have been a subject of intense study and numerous formulations have been proposed. Most of these can be described as separable, meaning that they apply a penalty to each element (or singular value) based on size, without considering the joint distribution. In this paper we present a class of non-separable penalties and give a recipe for computing strong relaxations suitable for optimization. In our analysis of this formulation we first give conditions that ensure that the globally optimal solution of the relaxation is the same as that of the original (unrelaxed) objective. We then show how a stationary point can be guaranteed to be unique under the RIP assumption (despite non-convexity of the framework). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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