Path-Following Methods

  • Renato Monteiro
  • Michael Todd
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 27)


In this chapter we study interior-point primal-dual path-following algorithms for solving the semidefinite programming (SDP) problem. In contrast to linear programming, there are several ways one can define the Newton-type search directions used by these algorithms. We discuss several ways in which this can done by motivating and introducing several search directions and families of directions. Polynomial convergence results for short- and long-step path-following algorithms using the Monteiro and Zhang family of directions are derived in detail; similar results are only surveyed, without proofs, for the Kojima, Shindoh and Hara family and the Monteiro and Tsuchiya family.


Search Direction Central Path Semidefinite Program Newton Step Newton Direction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Renato Monteiro
  • Michael Todd

There are no affiliations available

Personalised recommendations