Convex optimization in R

Roger Koenker, Ivan Mizera

Research output: Contribution to journalArticlepeer-review


Convex optimization now plays an essential role in many facets of statistics. We briefly survey some recent developments and describe some implementations of these methods in R. Applications of linear and quadratic programming are introduced including quantile regression, the Huber M-estimator and various penalized regression methods. Applications to additively separable convex problems subject to linear equality and inequality constraints such as nonparametric density estimation and maximum likelihood estimation of general nonparametric mixture models are described, as are several cone programming problems. We focus throughout primarily on implementations in the R environment that rely on solution methods linked to R, like MOSEK by the package Rmosek. Code is provided in R to illustrate several of these problems. Other applications are available in the R package REBayes, dealing with empirical Bayes estimation of nonparametric mixture models.

Original languageEnglish (US)
JournalJournal of Statistical Software
Issue number5
StatePublished - Sep 1 2014
Externally publishedYes


  • Convexity
  • Lasso
  • Linear programming
  • Optimization
  • Penalty methods
  • Quadratic programming
  • Quantile regression
  • Second order cone programming
  • Semidefinite programming
  • Shape-constrained methods

ASJC Scopus subject areas

  • Software
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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