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== SemiDefinite Matrices == | == SemiDefinite Matrices == |
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{{{#!latex2 Let $M(x):\mathbb{R}^m \rightarrow \mathbb{R}$ }}} |
The following is taken from page 9 of Cousot05VMCAI reference - see my bibtex. Suppose you have a loop in a program where the values of the variable values at the start of the loop are denoted Let with symmetric matrices Somehow I believe that where |
SemiDefinite What?
This page contains definitions for SemiDefinite things like matrices, programs, etc.
SemiDefinite Matrices
A positive SemiDefinite matrix is a HermitianMatrix all of whose eigenvalues are nonnegative. Thus any symmetric matrix that has a 0 on the diagonal is a SemiDefinite matrix.
SemiDefinite Programming
The following is taken from page 9 of Cousot05VMCAI reference - see my bibtex.
Suppose you have a loop in a program where the values of the variable values at the start of the loop are denoted $$x_0 \in \mathbb{R}n
Let
with symmetric matrices
$$$M(x) \succeq 0 \equiv \forall X \in \mathbb{R}N : XM(x)X{\top} \ge 0$$$
Somehow I believe that
$$$\left\{\begin{array}{l} \exists x \in \mathbb{R}m : M(x) \succeq 0 \\ Minimizing~~c{\top} x \end{array}\right.$$$
where