Convex approximations to sparse PCA via Lagrangian duality

Ronny Luss*, Marc Teboulle

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We derive a convex relaxation for cardinality constrained Principal Component Analysis (PCA) by using a simple representation of the L1 unit ball and standard Lagrangian duality. The resulting convex dual bound is an unconstrained minimization of the sum of two nonsmooth convex functions. Applying a partial smoothing technique reduces the objective to the sum of a smooth and nonsmooth convex function for which an efficient first order algorithm can be applied. Numerical experiments demonstrate its potential.

Original languageEnglish
Pages (from-to)57-61
Number of pages5
JournalOperations Research Letters
Issue number1
StatePublished - Jan 2011


FundersFunder number
Bloom's Syndrome Foundation2008-100
Iowa Science Foundation489-06
United States-Israel Binational Science Foundation
Israel Science Foundation


    • Convex programming
    • Lagrangian duality
    • Sparse Principal Component Analysis


    Dive into the research topics of 'Convex approximations to sparse PCA via Lagrangian duality'. Together they form a unique fingerprint.

    Cite this