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. ...
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...
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, ...
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...
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...