Asymptotic analysis of the exponential penalty trajectory in linear programming

R. Cominetti, J. San Martín

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

We consider the linear program min{c′x: Ax≤b} and the associated exponential penalty function fr(x) = c′x + rΣexp[(Aix - bi)/r]. For r close to 0, the unconstrained minimizer x(r) of fr admits an asymptotic expansion of the form x(r) = x* + rd* + η(r) where x* is a particular optimal solution of the linear program and the error term η(r) has an exponentially fast decay. Using duality theory we exhibit an associated dual trajectory λ(r) which converges exponentially fast to a particular dual optimal solution. These results are completed by an asymptotic analysis when r tends to ∞: the primal trajectory has an asymptotic ray and the dual trajectory converges to an interior dual feasible solution.

Original languageEnglish
Pages (from-to)169-187
Number of pages19
JournalMathematical Programming
Volume67
Issue number1-3
DOIs
StatePublished - Oct 1994

Keywords

  • Asymptotic expansion
  • Exponential penalty
  • Interior point methods
  • Linear programming
  • Optimal trajectory

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