A New Computational Method for the Sparsest Solutions to Systems of Linear Equations

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985556%3A_____%2F15%3A00448595" target="_blank" >RIV/67985556:_____/15:00448595 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1137/140968240" target="_blank" >http://dx.doi.org/10.1137/140968240</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1137/140968240" target="_blank" >10.1137/140968240</a>

Result language
angličtina
Original language name
A New Computational Method for the Sparsest Solutions to Systems of Linear Equations
Original language description
The connection between the sparsest solution to an underdetermined system of linear equations and the weighted l(1)-minimization problem is established in this paper. We show that seeking the sparsest solution to a linear system can be transformed to searching for the densest slack variable of the dual problem of weighted l(1)-minimization with all possible choices of nonnegative weights. Motivated by this fact, a new reweighted l(1)-algorithm for the sparsest solutions of linear systems, going beyond the framework of existing sparsity-seeking methods, is proposed in this paper. Unlike existing reweighted l(1)-methods that are based on the weights defined directly in terms of iterates, the new algorithm computes a weight in dual space via certain convex optimization and uses such a weight to locate the sparsest solutions. It turns out that the new algorithm converges to the sparsest solutions of linear systems under some mild conditions that do not require the uniqueness of the sparses
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
<a href="/en/project/GAP201%2F12%2F0671" target="_blank" >GAP201/12/0671: Variational and numerical analysis in nonsmooth continuum mechanics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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