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Results tagged with semidefinite-programming
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user 5963
Semidefinite programming can be regarded as an extension of linear programming. In a semidefinite program, the goal is to optimize a linear function over the intersection of the cone of positive semidefinite matrices with some affine space.
4
votes
Accepted
Full rank submatrices of positive semidefinite matrix
Yes, this is true. To see this note that for $A$ positive semidefinite, $v^T A v = 0$ if and only if $Av = 0$. For the less obvious direction, write $A = B^TB$ for a real matrix $B$. Then $0 = v^TA …
- 8,501
4
votes
how to determine a biquadratic form is positive-definite
In general one doesn't expect to have nice necessary and sufficient conditions for checking positivity of a biquadratic form. The sum-of-squares methods outlined in these course notes provide an effi …
- 8,501
2
votes
Accepted
Standard solution to semidefinite program
I will assume throughout that the definition of positive semidefiniteness includes symmetry. The problem is to find the Euclidean projection of $b$ onto the convex set $R = \{Qa \mid Q\succeq 0\}$. …
- 8,501