Mathematical Programming

, Volume 49, Issue 1, pp 7–21

Polynomial affine algorithms for linear programming

  • Clovis C. Gonzaga

DOI: 10.1007/BF01588776

Cite this article as:
Gonzaga, C.C. Mathematical Programming (1990) 49: 7. doi:10.1007/BF01588776


The method of steepest descent with scaling (affine scaling) applied to the potential functionq logc′x — ∑i=1n logxi solves the linear programming problem in polynomial time forq ⩾ n. Ifq = n, then the algorithm terminates in no more than O(n2L) iterations; if q ⩾ n +\(\sqrt n \) withq = O(n) then it takes no more than O(nL) iterations. A modified algorithm using rank-1 updates for matrix inversions achieves respectively O(n4L) and O(n3.5L) arithmetic computions.

Key words

Linear programmingaffine algorithmsKarmarkar's algorithminterior methods

Copyright information

© The Mathematical Programming Society, Inc. 1990

Authors and Affiliations

  • Clovis C. Gonzaga
    • 1
  1. 1.Department of Systems Engineering and Computer SciencesCOPPE-Federal University of Rio de JaneiroRio de JaneiroBrasil