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Lemma 1: Let { Â * , Γ(m) βkk * , Î * kk , P (m) kk * } be a local minimizer of Q1, then there exists a local minimizer { Â * * , Γ(m) βkk * * , Î * * kk , P (m) kk * * } of Q2, such that α * kk Γ(m) βkk * = α * * kk Γ(m) βkk * * and ιkk i,j * ρkk(m) i,j * = ιkk i,j * * ρkk(m) i,j * * . Similarly, let { Â * * , Γ(m) βkk * * , Î * * kk , P (m) kk * * } be a local minimizer of Q2, then there exists a local minimizer { Â * , Γ(m) βkk * , Î * kk , P (m) kk * } of Q1, such that α * kk Γ(m) βkk * = α * * kk Γ(m) βkk * * and ιkk i,j * ρkk(m) i,j * = ιkk i,j * * ρkk(m) i,j * * . Proof: Suppose { Â * , Γ(m) βkk * , Î * kk , P (m) kk * } is a local minimizer of Q1. We would like to prove { Â * * = * * = Ω(m) kk * * / η 12 M m=1 | Ω(m) kk * * | 1 ,

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