Constraint aggregation principle in convex optimization

Yuri M. Ermoliev, Arkadii V. Kryazhimskii, Andrzej Ruszczyński

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

A general constraint aggregation technique is proposed for convex optimization problems. At each iteration a set of convex inequalities and linear equations is replaced by a single surrogate inequality formed as a linear combination of the original constraints. After solving the simplified subproblem, new aggregation coefficients are calculated and the iteration continues. This general aggregation principle is incorporated into a number of specific algorithms. Convergence of the new methods is proved and speed of convergence analyzed. Next, dual interpretation of the method is provided and application to decomposable problems is discussed. Finally, a numerical illustration is given.

Original languageEnglish (US)
Pages (from-to)353-372
Number of pages20
JournalMathematical Programming, Series B
Volume76
Issue number3
DOIs
StatePublished - Mar 1 1997
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • Mathematics(all)

Keywords

  • Decomposition
  • Nonsmooth optimization
  • Subgradient methods
  • Surrogate constraints

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