Before revision:  For the related "\ell_\infty-gap problem", where A is either PSD or has an eigenvalue satisfying \lambda_i(A) <\succeq 0} \|\mathbf{A}} - \epsilon n, our algorithm only requires\|_2 > \epsilon n.
After revision:  For the related "\ell_\infty-gap problem", where A is either PSD or satisfies \min_{\mathbf{B\succeq 0} \|\mathbf{A}} - \epsilon n, our algorithm only requires\|_2 > \epsilon n.