On the convergence of the exponential multiplier method for convex programming

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121 Scopus citations


In this paper, we analyze the exponential method of multipliers for convex constrained minimization problems, which operates like the usual Augmented Lagrangian method, except that it uses an exponential penalty function in place of the usual quadratic. We also analyze a dual counterpart, the entropy minimization algorithm, which operates like the proximal minimization algorithm, except that it uses a logarithmic/entropy "proximal" term in place of a quadratic. We strengthen substantially the available convergence results for these methods, and we derive the convergence rate of these methods when applied to linear programs.

Original languageEnglish (US)
Pages (from-to)1-19
Number of pages19
JournalMathematical Programming
Issue number1-3
StatePublished - Jun 1993
Externally publishedYes


  • Augmented Lagrangian
  • Convex programming
  • exponential penalty
  • linear programming
  • multiplier method

ASJC Scopus subject areas

  • Software
  • Mathematics(all)


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