Extension of primal-dual interior point algorithms to symmetric cones

By S. Schmieta, F. Alizadeh. Mathematical programming, 2003

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Some P-properties for linear transformations on Euclidean Jordan algebras (2004, background): “We note that the above system is the primal-dual optimal solution system corresponding to the (following) primal-dual pair of linear programs over the symmetric cone K [32]: (Primal) min {〈c, x〉 : Ax = b, x ∈ K}, and (Dual) max {〈b, y〉 : ATy + s = c, s ∈ K, y ∈ Rn}.”
Jordan algebraic approach to symmetric optimization (2007, background): “Later, Schmieta and Alizadeh [47] showed that the so-called commutative class of primal-dual interior-point algorithms which were designed by Monteiro and Zhang for semi-de nite optimization [35] extends word-byword to all symmetric cones.”
Computation (2020, neutral): “(cid:2971) (cid:3168)(cid:3169) (cid:3416) The comprehensive clustering coefﬁcient σ ki for group i, in which i = 1, 2 . . . n , in the grey class k , k = 1, 2 . . . s , is calculated by (4). of the j th criterion, and \ j is the weight of criterion j [7].”