A first order method for finding minimal norm-like solutions of convex optimization problems

Amir Beck, Shoham Sabach

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a general class of convex optimization problems in which one seeks to minimize a strongly convex function over a closed and convex set which is by itself an optimal set of another convex problem. We introduce a gradient-based method, called the minimal norm gradient method, for solving this class of problems,and establish the convergence of the sequence generated by the algorithm as well as a rate of convergence of the sequence of function values. The paper ends with several illustrating numerical examples

Original languageEnglish
Pages (from-to)25-46
Number of pages22
JournalMathematical Programming
Volume147
Issue number1
DOIs
StatePublished - 2014
Externally publishedYes

Keywords

  • Bilevel optimization
  • Complexity analysis
  • Convex minimization
  • Minimal norm solution

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