Necessary conditions for uniqueness in L1-approximation

Necessary Conditions for Uniqueness in L ’ - Approximation

Let K be a compact subset of R " with K=~nt K. Necessary conditions on an n-dimensional subspace U, of C(K) are given so that for each f~ C(K) there exists a unique best L'(w)-approximation from U,,, for every fixed positive weight function w. Let K be a compact subset of R ". For convenience we assume that K= int K. W will denote the set of bounded, integrable functions on K for which inf(w(x)...

Necessary and sufficient conditions of solution uniqueness in ℓ1 minimization

This paper shows that the solutions to various convex `1 minimization problems are unique if and only if a common set of conditions are satisfied. This result applies broadly to the basis pursuit model, basis pursuit denoising model, Lasso model, as well as other `1 models that either minimize f(Ax − b) or impose the constraint f(Ax − b) ≤ σ, where f is a strictly convex function. For these mod...

Necessary and sufficient conditions for uniqueness of the minimum in Prediction Error Identification

The contribution of this paper is to establish computable necessary and sufficient conditions on the model structure and on the experiment under which the Prediction Error Identification (PEI) criterion has a unique global minimum. We consider a broad class of rational model structures whose numerator and denominator are affine in the unknown parameter vector; this class encompasses all classic...

Some Results on Necessary Conditions for Tow Quasidifferentiable Optimization Problems

New Necessary Conditions for

In this paper, we obtain several nonexistence results for abelian Hadamard diier-ence sets. In particular, we prove that there are no Hadamard diierence sets in abelian groups G = Z 2 Z 2 P , where jPj = p 2 , is odd and p is a prime congruent to 1(mod 4). Also we give a detailed proof for a connection between certain reversible Hadamard diierence sets and projective three-weight codes which wa...