The KKT System

Robert J. Vanderbei
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Robert J. Vanderbei: Princeton University

Chapter Chapter 19 in Linear Programming, 2014, pp 285-291 from Springer

Abstract: Abstract 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: 19.1 A Δ x + Δ w = ρ $$\displaystyle\begin{array}{rcl} A\Delta x + \Delta w& =& \rho {}\end{array}$$ 19.2 A T Δ y − Δ z = σ $$\displaystyle\begin{array}{rcl}{ A}^{T}\Delta y - \Delta z& =& \sigma {}\end{array}$$ 19.3 Z Δ x + X Δ z = μ e − X Z e $$\displaystyle\begin{array}{rcl} Z\Delta x + X\Delta z& =& \mu e - XZe{}\end{array}$$ 19.4 W Δ y + Y Δ w = μ e − Y W e . $$\displaystyle\begin{array}{rcl} W\Delta y + Y \Delta w& =& \mu e - Y We.{}\end{array}$$

Keywords: Step Direction Vector; Path-following Method; Time-consuming Aspect; Dense Rows; Karush–Kuhn–Tucker System (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-1-4614-7630-6_19

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