Ee 227a: Convex Optimization and Applications 11.2 Sdp Duality
نویسندگان
چکیده
The standard model for the Semi Definite Programming (SDP) is min c T x s.t. F (x) = F 0 + m i=1 x i F i 0, where each of the F i 's are symmetric matrices. We define the Lagrangian: L(x, Z) = c T x − Tr(ZF (x)), where the dual variable Z is a psd matrix. The Lagrangian is constructed so that max Z0 L(x, Z) = c T x if F (x) 0, +∞ otherwise. Thus, we can express p * as the solution to an unconstrained problem: p * = min x max Z0 L(x, Z) The dual problem is d * = max Z0 min x L(x, Z).
منابع مشابه
EE 227 A : Convex Optimization and Applications February 21 , 2012 Lecture 11 : SDP Duality
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