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Let C = [ A = 0 The primal and dual semidefinite programs are min s.t. trace(CX) trace(A;X) A2 := [ 1 1 2

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Let C = [ A = 0 The primal and dual semidefinite programs are min s.t. trace(CX) trace(A;X) A2 := [ 1 1 2 " b = [ 3 ] max bTy = bi = 2 (P) s.t. i=1 Aiyi S = 0 X 02 0 S (D) Show that (P) has an optimal value of 9. Is (D) strictly feasible? Show that y = (-1, 2) is optimal for (D). Show that the optimal X and S matrices are simultaneously diagonalizable.

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