v2006.03.09 - Convex Optimization

6.3. RANK REDUCTION 383Initialize:C =I , ρ=3, A j ∆ = δ(A(j, :)) , j =1, 2, 3, X ⋆ = δ(x M) , m=3, n=5.{Iteration i=1:⎡Step 1: R 1 =⎢⎣√21280 00 0 00√501280 0√00 090128⎤.⎥⎦find Z 1 ∈ S 3subject to 〈Z 1 , R T 1A j R 1 〉 = 0, j =1, 2, 3(923)A nonzero randomly selected matrix Z 1 having 0 main diagonalis feasible and yields a nonzero perturbation matrix. Choose,arbitrarily,Z 1 = 11 T − I ∈ S 3 (924)then (rounding)⎡B 1 =⎢⎣Step 2: t ⋆ 1= 1 because λ(Z 1 )=[−1 −1⎡X ⋆ ← δ(x M) + B 1 =⎢⎣0 0 0.0247 0 0.10480 0 0 0 00.0247 0 0 0 0.16570 0 0 0 00.1048 0 0.1657 0 02 ] T . So,⎤⎥⎦20 0.0247 0 0.10481280 0 0 0 00.0247 051280 0.16570 0 0 0 00.1048 0 0.1657 090128⎤(925)⎥⎦ (926)has rank ρ ←1 and produces the same optimal objective value.}