Dimensionality reduction of SDPs through sketching

Research output: Contribution to journalJournal articleResearchpeer-review

We show how to sketch semidefinite programs (SDPs) using positive maps in order to reduce their dimension. More precisely, we use Johnson–Lindenstrauss transforms to pro- duce a smaller SDP whose solution preserves feasibility or approximates the value of the original problem with high probability. These techniques allow to improve both complexity and storage space requirements. They apply to problems in which the Schatten 1-norm of the matrices specifying the SDP and also of a solution to the problem is constant in the problem size. Furthermore, we provide some results which clarify the limitations of positive, linear sketches in this setting.
Original languageEnglish
JournalLinear Algebra and Its Applications
Pages (from-to)461-475
Number of pages15
Publication statusPublished - 15 Feb 2019
Externally publishedYes

    Research areas

  • Dimensionality reduction, Johnson–Lindenstrauss transforms, Semidefinite programming, Sketching

ID: 231872633