User talk:Karthikraoa

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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
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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:
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(Dn is the space of diagonal matrices and Sn is the space of symmetric matrices)
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<math>\mathbb{S}^n</math> is the space of <math>n\times n</math> symmetric matrices.
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<math>\,g</math> is a vector.
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<math>\,\delta(g)</math> is a diagonal matrix whose main diagonal is <math>g</math>
<br>
<br>
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<math>\begin{array}{rl}\mbox{find}&X\in S_n~, ~G\in D_n\\
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<math>\begin{array}{rl}\mbox{find}&X\in\mathbb{S}^n\\
\mbox{subject to}
\mbox{subject to}
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& A\,\mbox{svec}X = b\\
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&A\,\mbox{svec}X = b\\
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&GXc = d\\
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&\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>

Revision as of 18:22, 1 December 2009

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

LaTeX: \mathbb{S}^n is the space of LaTeX: n\times n symmetric matrices.

LaTeX: \,g is a vector.

LaTeX: \,\delta(g) is a diagonal matrix whose main diagonal is LaTeX: g


LaTeX: \begin{array}{rl}\mbox{find}&X\in\mathbb{S}^n\\ \mbox{subject to} &A\,\mbox{svec}X = b\\ &\delta(g)Xc = d\\ &X\succeq 0\\ &\mbox{rank}X\le r \end{array}

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