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On Convex Envelopes...
On Convex Envelopes and Regularization of Non-convex Functionals Without Moving Global Minima
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- Carlsson, Marcus (författare)
- Lund University,Lunds universitet,Matematik (naturvetenskapliga fakulteten),Matematikcentrum,Institutioner vid LTH,Lunds Tekniska Högskola,Mathematics (Faculty of Sciences),Centre for Mathematical Sciences,Departments at LTH,Faculty of Engineering, LTH
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(creator_code:org_t)
- 2019-05-29
- 2019
- Engelska.
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Ingår i: Journal of Optimization Theory and Applications. - : Springer Science and Business Media LLC. - 0022-3239 .- 1573-2878. ; 183:1, s. 66-84
- Relaterad länk:
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Abstract
Ämnesord
Stäng
- We provide theory for the computation of convex envelopes of non-convex functionals including an ℓ2-term and use these to suggest a method for regularizing a more general set of problems. The applications are particularly aimed at compressed sensing and low-rank recovery problems, but the theory relies on results which potentially could be useful also for other types of non-convex problems. For optimization problems where the ℓ2-term contains a singular matrix, we prove that the regularizations never move the global minima. This result in turn relies on a theorem concerning the structure of convex envelopes, which is interesting in its own right. It says that at any point where the convex envelope does not touch the non-convex functional, we necessarily have a direction in which the convex envelope is affine.
Ämnesord
- NATURVETENSKAP -- Matematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics (hsv//eng)
Nyckelord
- Convex envelope
- Fenchel conjugate
- Non-convex/non-smooth optimization
- Proximal hull
- Regularization
Publikations- och innehållstyp
- art (ämneskategori)
- ref (ämneskategori)
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