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\end{pmatrix} \succeq 0
\end{array}</math>
We set <math>\rho_{AB} = x_{12}, \ \rho_{AC} = x_{13}, \ \rho_{BC} = x_{23} </math> to obtain the answer. This can be formulated by an SDP. We handle the inequality constraints by augmenting the variable matrix and introducing [[slack variable]]s, for example
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=== Interior point methods ===
Most codes are based on [[interior point methods]] (CSDP, [[MOSEK]], SeDuMi, [https://www.math.cmu.edu/~reha/sdpt3.html SDPT3], DSDP, SDPA). Robust and efficient for general linear SDP problems. Restricted by the fact that the algorithms are second-order methods and need to store and factorize a large (and often dense) matrix. Theoretically, the state-of-the-art high-accuracy SDP algorithms<ref>{{Cite journal |last=Jiang |first=Haotian |last2=Kathuria |first2=Tarun |last3=Lee |first3=Yin Tat |last4=Padmanabhan |first4=Swati |last5=Song |first5=Zhao |date=November 2020
=== First-order methods ===
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