Affine-scaling for linear programs with free variables

R. J. Vanderbei

Research output: Contribution to journalArticlepeer-review

31 Scopus citations


The affine-scaling modification of Karmarkar's algorithm is extended to solve problems with free variables. This extended primal algorithm is used to prove two important results. First the geometrically elegant feasibility algorithm proposed by Chandru and Kochar is the same algorithm as the one obtained by appending a single column of residuals to the constraint matrix. Second the dual algorithm as first described by Adler et al., is the same as the extended primal algorithm applied to the dual.

Original languageEnglish (US)
Pages (from-to)31-44
Number of pages14
JournalMathematical Programming
Issue number1-3
StatePublished - Jan 1989
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Software
  • General Mathematics


  • Affine-scaling
  • Karmarkar's algorithm
  • dual algorithm
  • feasibility algorithm


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