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== Applications ==
Semidefinite programming has been applied to find approximate solutions to combinatorial optimization problems, such as the solution of the [[max cut]] problem with an [[approximation ratio]] of 0.87856. SDPs are also used in geometry to determine tensegrity graphs, and arise in control theory as [[Linear matrix inequality|LMIs]], and in inverse elliptic coefficient problems as convex, non-linear, semidefiniteness constraints.<ref>{{citation|last1=Harrach|first1=Bastian|date=2021|title=Solving an inverse elliptic coefficient problem by convex non-linear semidefinite programming|journal=Optimization Letters|volume=16 |issue=5 |pages=1599–1609 |language=en|doi=10.1007/s11590-021-01802-4|arxiv=2105.11440|s2cid=235166806}}</ref> It is also widely used in physics to constrain [[Conformal field theory|conformal field theories]] with the [[conformal bootstrap]].<ref>{{cite
== References ==
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