Dattorro Convex Optimization of Eternity II

(Difference between revisions)

Revision as of 00:38, 31 January 2011

This Matlab binary contains matrices $LaTeX: \,E$ and $LaTeX: \,t$ .

I regard the following as a very difficult problem, having spent considerable time with it.

$LaTeX: \begin{array}{cl}\mbox{minimize}_x&c^{\rm T}x\\ \mbox{subject to}&E\,x=t\\ &x\geq_{}\mathbf{0}\end{array}$

Matrix $LaTeX: E\!\in\!\mathbb{R}^{10054\times204304}$ is sparse having only 1,170,516 nonzeros.

All its entries are integers from the set $LaTeX: \{{-1},0,1\}\,$ .

Vector $LaTeX: c\,$ is left unspecified because it is varied later as part of a Convex Iteration.

Vector $LaTeX: c\,$ may arbitrarily be set to $LaTeX: \mathbf{0}$ or $LaTeX: \mathbf{1}$ .

@@ Line 4: / Line 4: @@
 <center>
-<math>\begin{array}{cl}\mbox{minimize}_{x\in\{0,1\}}&c^{\rm T}x\\
+<math>\begin{array}{cl}\mbox{minimize}_x&c^{\rm T}x\\
 \mbox{subject to}&E\,x=t\\
 &x\geq_{}\mathbf{0}\end{array}</math>