Abstract
Information geometry is used to elucidate convex optimization problems under L1 constraint. A convex function induces a Riemannian metric and two dually coupled affine connections in the manifold of parameters of interest. A generalized Pythagorean theorem and projection theorem hold in such a manifold. An extended LARS algorithm, applicable to both under-determined and over-determined cases, is studied and properties of its solution path are given. The algorithm is shown to be a Minkovskian gradient-descent method, which moves in the steepest direction of a target function under the Minkovskian L 1 norm. Two dually coupled affine coordinate systems are useful for analyzing the solution path.
Original language | English |
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Article number | 6414587 |
Pages (from-to) | 576-585 |
Number of pages | 10 |
Journal | IEEE Journal on Selected Topics in Signal Processing |
Volume | 7 |
Issue number | 4 |
DOIs | |
Publication status | Published - 2013 |
Externally published | Yes |
Keywords
- Extended LARS
- L1-constraint
- information geometry
- sparse convex optimization
ASJC Scopus subject areas
- Signal Processing
- Electrical and Electronic Engineering