Necessary and Sufficient Condition
George Thomas Kurian · The Encyclopedia of Political Science · 2011
A family of regularization functionals is said to admit a linear representer theorem if every member of the family admits minimizers that lie in a fixed finite dimensional subspace.A recent characterization states that a general class of regularization functionals with differentiable regularizer admits a linear representer theorem if and only if the regularization term is a non-decreasing function of the norm.In this report, we improve over such result by replacing the differentiability assumption with lower semicontinuity and deriving a proof that is independent of the dimensionality of the space.