Dattorro Convex Optimization of Eternity II

(Difference between revisions)

Revision as of 19:58, 13 February 2011

This Matlab binary contains matrices

$LaTeX: \,\tilde{E}\!\in\!\mathbb{R}^{10054\times204304}$ and $LaTeX: \,\tilde{\tau}\in\!\mathbb{R}^{10054}$

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

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

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

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

$LaTeX: \tilde{\tau}\in\{0,1\}^{10054}$ .

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 1: / Line 1: @@
-This [http://www.convexoptimization.com/TOOLS/Wotao.Yin/EternityII.mat Matlab binary] contains matrices <math>\,E</math> and <math>\,t</math>.
+This [http://www.convexoptimization.com/TOOLS/Wotao.Yin/EternityII.mat Matlab binary] contains matrices
+*<math>\,\tilde{E}\!\in\!\mathbb{R}^{10054\times204304}</math> and <math>\,\tilde{\tau}\in\!\mathbb{R}^{10054}</math>
 I regard the following as a very difficult problem, having spent considerable time with it.
@@ Line 5: / Line 6: @@
 <center>
 <math>\begin{array}{cl}\mbox{minimize}_x&c^{\rm T}x\\
-\mbox{subject to}&E\,x=t\\
+\mbox{subject to}&\tilde{E}\,x=\tilde{\tau}\\
 &x\succeq_{}\mathbf{0}\end{array}</math>
 </center>
-Matrix <math>E\!\in\!\mathbb{R}^{10054\times204304}</math> is sparse having only 1,170,516 nonzeros.
+Matrix <math>\tilde{E}\!\in\!\mathbb{R}^{10054\times204304}</math> is sparse having only 1,170,516 nonzeros.
-All entries of <math>E\,</math> are integers from the set <math>\{{-1},0,1\}\,</math>.
+All entries of <math>\tilde{E}\,</math> are integers from the set <math>\{{-1},0,1\}\,</math>.
-<math>t\in\{0,1\}^{10054}</math>.
+<math>\tilde{\tau}\in\{0,1\}^{10054}</math>.
 Vector <math>c\,</math> is left unspecified because it is varied later as part of a