User talk:Karthikraoa - Revision history

Dattorro at 01:26, 2 December 2009

2009-12-02T01:26:14Z

←Older revision		Revision as of 01:26, 2 December 2009
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	<br>		<br>
-	<math>\begin{array}{rl}\mbox{find}&X\in\mathbb{S}^n\\	+	<math>\begin{array}{rl}\mbox{find}&X\!\in\mathbb{S}^n, ~g\in\mathbb{R}^n\\
	\mbox{subject to}		\mbox{subject to}
	&A\,\mbox{svec}X = b\\		&A\,\mbox{svec}X = b\\

Dattorro at 01:24, 2 December 2009

2009-12-02T01:24:51Z

←Older revision		Revision as of 01:24, 2 December 2009
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-	The following is a problem very similar to the problem "Convex Iteration rank-1" in Jon ~~Dattoro~~'s book CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY:	+	The following is a problem very similar to the problem "Convex Iteration rank-1" in Jon Dattorro's book CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY:

	<math>\mathbb{S}^n</math> is the space of <math>n\times n</math> symmetric matrices.		<math>\mathbb{S}^n</math> is the space of <math>n\times n</math> symmetric matrices.

Dattorro at 01:24, 2 December 2009

2009-12-02T01:24:15Z

←Older revision		Revision as of 01:24, 2 December 2009
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	<math>\,g</math> is a vector.		<math>\,g</math> is a vector.

-	<math>\,\delta(g)</math> is a diagonal matrix whose main diagonal is <math>g</math>	+	<math>\,\delta(g)</math> is a diagonal matrix whose main diagonal is <math>\,g.</math>

	<br>		<br>

Dattorro at 01:22, 2 December 2009

2009-12-02T01:22:38Z

←Older revision		Revision as of 01:22, 2 December 2009
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-	The following is a problem very similar to the problem "Convex Iteration rank-1" in Jon Dattoro's book CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY	+	The following is a problem very similar to the problem "Convex Iteration rank-1" in Jon Dattoro's book CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY:

-	~~(Dn~~ is the space of ~~diagonal~~ matrices ~~and Sn~~ is ~~the space of symmetric matrices~~)	+	<math>\mathbb{S}^n</math> is the space of <math>n\times n</math> symmetric matrices.
		+
		+	<math>\,g</math> is a vector.
		+
		+	<math>\,\delta(g)</math> is a diagonal matrix whose main diagonal is <math>g</math>

	<br>		<br>
-	<math>\begin{array}{rl}\mbox{find}&X\in ~~S_n~, ~G~~\~~in D_n~~\\	+	<math>\begin{array}{rl}\mbox{find}&X\in\mathbb{S}^n\\
	\mbox{subject to}		\mbox{subject to}
-	& A\,\mbox{svec}X = b\\	+	&A\,\mbox{svec}X = b\\
-	&~~GXc~~ = d\\	+	&\delta(g)Xc = d\\
	&X\succeq 0\\		&X\succeq 0\\
	&\mbox{rank}X\le r		&\mbox{rank}X\le r
	\end{array}</math>		\end{array}</math>

Dattorro at 01:15, 2 December 2009

2009-12-02T01:15:10Z

←Older revision		Revision as of 01:15, 2 December 2009
Line 8:		Line 8:
	& A\,\mbox{svec}X = b\\		& A\,\mbox{svec}X = b\\
	&GXc = d\\		&GXc = d\\
-	&X\ge 0\\	+	&X\succeq 0\\
	&\mbox{rank}X\le r		&\mbox{rank}X\le r
	\end{array}</math>		\end{array}</math>

Dattorro at 00:48, 2 December 2009

2009-12-02T00:48:36Z

←Older revision		Revision as of 00:48, 2 December 2009
Line 6:		Line 6:
	<math>\begin{array}{rl}\mbox{find}&X\in S_n~, ~G\in D_n\\		<math>\begin{array}{rl}\mbox{find}&X\in S_n~, ~G\in D_n\\
	\mbox{subject to}		\mbox{subject to}
-	& A\,svec X = b\\	+	& A\,\mbox{svec}X = b\\
	&GXc = d\\		&GXc = d\\
	&X\ge 0\\		&X\ge 0\\
	&\mbox{rank}X\le r		&\mbox{rank}X\le r
	\end{array}</math>		\end{array}</math>

Dattorro: New page: The following is a problem very similar to the problem "Convex Iteration rank-1" in Jon Dattoro's book CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY (Dn is the space of diagonal mat...

2009-12-02T00:45:18Z

New page: The following is a problem very similar to the problem "Convex Iteration rank-1" in Jon Dattoro's book CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY (Dn is the space of diagonal mat...

New page

The following is a problem very similar to the problem "Convex Iteration rank-1" in Jon Dattoro's book CONVEX OPTIMIZATION & EUCLIDEAN DISTANCE GEOMETRY

(Dn is the space of diagonal matrices and Sn is the space of symmetric matrices)

<br>
<math>\begin{array}{rl}\mbox{find}&X\in S_n~, ~G\in D_n\\
\mbox{subject to}
& A\,svec X = b\\
&GXc = d\\
&X\ge 0\\
&\mbox{rank}X\le r
\end{array}</math>