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» Convexity, Duality and Effects
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ORL
2011
12 years 11 months ago
Convex approximations to sparse PCA via Lagrangian duality
We derive a convex relaxation for cardinality constrained Principal Component Analysis (PCA) by using a simple representation of the L1 unit ball and standard Lagrangian duality. ...
Ronny Luss, Marc Teboulle
JGO
2010
117views more  JGO 2010»
13 years 3 months ago
Machine learning problems from optimization perspective
Both optimization and learning play important roles in a system for intelligent tasks. On one hand, we introduce three types of optimization tasks studied in the machine learning l...
Lei Xu
SIAMJO
2008
84views more  SIAMJO 2008»
13 years 4 months ago
Regularity Conditions via Quasi-Relative Interior in Convex Programming
We give some new regularity conditions for Fenchel duality in separated locally convex vector spaces, written in terms of the notion of quasi interior and quasi-relative interior, ...
Radu Ioan Bot, Ernö Robert Csetnek, Gert Wank...
MP
2007
76views more  MP 2007»
13 years 4 months ago
Universal duality in conic convex optimization
Given a primal-dual pair of linear programs, it is well known that if their optimal values are viewed as lying on the extended real line, then the duality gap is zero, unless both...
Simon P. Schurr, André L. Tits, Dianne P. O...
MOC
2000
88views more  MOC 2000»
13 years 4 months ago
A posteriori error estimation for variational problems with uniformly convex functionals
The objective of this paper is to introduce a general scheme for deriving a posteriori error estimates by using duality theory of the calculus of variations. We consider variationa...
Sergey I. Repin