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Potential Reduction Algorithms Kurt M. Anstreicher
 

Summary: Potential Reduction Algorithms
Kurt M. Anstreicher
Department of Management Sciences
University of Iowa
Iowa City, IA 52242, USA
1 Introduction
Potential reduction algorithms have a distinguished role in the area of in-
terior point methods for mathematical programming. Karmarkar's [44] al-
gorithm for linear programming, whose announcement in 1984 initiated a
torrent of research into interior point methods, used three key ingredients: a
non­standard linear programming formulation, projective transformations,
and a potential function with which to measure the progress of the algorithm.
It was quickly shown that the non­standard formulation could be avoided,
and eventually algorithms were developed that eliminated the projective
transformations, but retained the use of a potential function. It is then fair
to say that the only really essential element of Karmarkar's analysis was the
potential function. Further modifications to Karmarkar's original potential
function gave rise to potential reduction algorithms having the state­of­the­
art theoretical complexity of O(

  

Source: Anstreicher, Kurt M. - Department of Computer Science, University of Iowa

 

Collections: Computer Technologies and Information Sciences