Browsing by Subject "Quadratic perturbation"

Filter results by typing the first few letters
Now showing 1 - 3 of 3
  • Thumbnail Image
    ItemOpen Access
    A global error bound for quadratic perturbation of linear programs
    (Elsevier, 2002) Pınar, M. C.
    We prove a global error bound result on the quadratic perturbation of linear programs. The error bound is stated in terms of function values.
  • Thumbnail Image
    ItemOpen Access
    Necessary and sufficient conditions for noiseless sparse recovery via convex quadratic splines
    (Society for Industrial and Applied Mathematics Publications, 2019) Pınar, Mustafa Ç.
    The problem of exact recovery of an individual sparse vector using the Basis Pursuit (BP) model is considered. A differentiable Huber loss function (a convex quadratic spline) is used to replace the $\ell_1$-norm in the BP model. Using the theory of duality and classical results from quadratic perturbation of linear programs, a necessary condition for exact recovery leading to a negative result is given. An easily verifiable sufficient condition is also presented.
  • Thumbnail Image
    ItemOpen Access
    Sparse solutions to an underdetermined system of linear equations via penalized Huber loss
    (Springer, 2020) Kızılkale, C.; Pınar, Mustafa Çelebi
    We investigate the computation of a sparse solution to an underdetermined system of linear equations using the Huber loss function as a proxy for the 1-norm and a quadratic error term à la Lasso. The approach is termed “penalized Huber loss”. The results of the paper allow to calculate a sparse solution using a simple extrapolation formula under a sign constancy condition that can be removed if one works with extreme points. Conditions leading to sign constancy, as well as necessary and sufficient conditions for computation of a sparse solution by penalized Huber loss, and ties among different solutions are presented.