exact and stable recovery

Sparse Recovery on Euclidean Jordan Algebras

  • Lingchen Kong
  • Jie Sun
  • Jiyuan Tao
  • Naihua Xiu
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    We consider the sparse recovery problem on Euclidean Jordan algebra (SREJA), which includes sparse signal recovery and low-rank symmetric matrix recovery as special cases. We introduce the restricted isometry property, null space property (NSP), and $s$-goodness for linear transformations in $s$-sparse element recovery on Euclidean Jordan algebra (SREJA), all of which provide sufficient conditions for … Read more

    S-semigoodness for Low-Rank Semidefinite Matrix Recovery

  • Lingchen Kong
  • Jie Sun
  • Naihua Xiu
    • Categories Convex Optimization, Semi-definite Programming Tags , , , ,

    We extend and characterize the concept of $s$-semigoodness for a sensing matrix in sparse nonnegative recovery (proposed by Juditsky , Karzan and Nemirovski [Math Program, 2011]) to the linear transformations in low-rank semidefinite matrix recovery. We show that s-semigoodness is not only a necessary and sufficient condition for exact $s$-rank semidefinite matrix recovery by a … Read more