Bundle methods for dual atomic pursuit
Abstract
The aim of structured optimization is to assemble a solution, using a given set of (possibly uncountably infinite) atoms, to fit a model to data. A two-stage algorithm based on gauge duality and bundle method is proposed. The first stage discovers the optimal atomic support for the primal problem by solving a sequence of approximations of the dual problem using a bundle-type method. The second stage recovers the approximate primal solution using the atoms discovered in the first stage. The overall approach leads to implementable and efficient algorithms for large problems.
- Publication:
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arXiv e-prints
- Pub Date:
- October 2019
- DOI:
- 10.48550/arXiv.1910.13650
- arXiv:
- arXiv:1910.13650
- Bibcode:
- 2019arXiv191013650F
- Keywords:
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- Mathematics - Optimization and Control
- E-Print:
- 53rd Annual Asilomar Conference on Signals, Systems, and Computers