The KKT System

  • Robert J. Vanderbei
Part of the International Series in Operations Research & Management Science book series (ISOR, volume 196)


The most time-consuming aspect of each iteration of the path-following method is solving the system of equations that defines the step direction vectors Δx, Δy, Δw, and Δz:
$$\displaystyle\begin{array}{rcl} A\Delta x + \Delta w& =& \rho {}\end{array}$$
$$\displaystyle\begin{array}{rcl}{ A}^{T}\Delta y - \Delta z& =& \sigma {}\end{array}$$
$$\displaystyle\begin{array}{rcl} Z\Delta x + X\Delta z& =& \mu e - XZe{}\end{array}$$
$$\displaystyle\begin{array}{rcl} W\Delta y + Y \Delta w& =& \mu e - Y We.{}\end{array}$$


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Robert J. Vanderbei
    • 1
  1. 1.Department of Operations Research and Financial EngineeringPrinceton UniversityPrincetonUSA

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