Semidefinite programming: Difference between revisions

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* A certificate that there is no feasible solution.
 
The run-time in the [[Real RAM]] model is, [[With high probability|with high probability,]], in <math>
O\left (\frac{N \cdot \log{n}\cdot \log{m} \cdot log(1/\epsilon)}{\epsilon^3}\right)
</math>, where ''N'' is input size (number of nonzero entries in the matrices), ''n'' is the number of variables, and ''m'' is the number of inequality constraints. Note that the runtime is polynomial in 1/''ε'' rather than log(1/''ε''). However, in practice it runs quite fast.
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* A certificate that no feasible solution exists.
 
The run-time in the [[Real RAM]] model is, [[With high probability|with high probability,]], in <math>
O\left (\frac{N \cdot \log{n}\cdot \log{m} \cdot }{\epsilon^3}\right)
</math>. The algorithm is applied in a [[binary search]] style to find an approximately-optimal solution.