Semidefinite programming: Difference between revisions

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in which case this matrix is called the [[correlation matrix]]. Suppose that we know from some prior knowledge (empirical results of an experiment, for example) that <math>-0.2 \leq \rho_{AB} \leq -0.1</math> and <math>0.4 \leq \rho_{BC} \leq 0.5</math>. The problem of determining the smallest and largest values that <math>\rho_{AC} \ </math> can take is given by:

:

:<math>\begin{array}{rl}

{\displaystyle\min/\max} & x_{13} \\

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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 journal |last=Simmons-Duffin |first=David |date=2015-02-06 |title=A Semidefinite Program Solver for the Conformal Bootstrap |url=http://arxiv.org/abs/1502.02033 |journal=arXiv:1502.02033 [cond-mat, physics:hep-th] |doi=10.48550/arxiv.1502.02033}}</ref>

. It is also widely used in physics to constrain [[Conformal field theory|conformal field theories]] with the [[conformal bootstrap]]<ref>{{Cite journal |last=Simmons-Duffin |first=David |date=2015-02-06 |title=A Semidefinite Program Solver for the Conformal Bootstrap |url=http://arxiv.org/abs/1502.02033 |journal=arXiv:1502.02033 [cond-mat, physics:hep-th] |doi=10.48550/arxiv.1502.02033}}</ref>.

== References ==