This question is not similar to this one or this as the values to be calculated are different.
This is the definition I am using:
$ H_{min}(A|B)= -lg (\lambda_{min}) $ (where $H_{min}$ is being determined for a density matrix $\rho_{AB}$)
$\lambda_{min}$ is the minimum positive value of $\lambda$ for which there exists a valid density matrix $\sigma_B$ that satisfies ${\rho}_{AB} \le \lambda(\mathbb{I}_A \otimes \sigma_B)$.
(A valid density matrix under the postulates given by quantum mechanics, which dictate that they are positive semi-definite, Hermitian operators of trace one.)
Is there a straightforward way to calculate the lambda value for a given $\rho_{AB}$? Example: $\rho_1= | \phi \rangle \langle \phi|$, $\rho_2= \frac{1}{2}\mathbb{I} + \frac{1}{2} | \phi \rangle \langle \phi|$ , where $|\phi\rangle= \frac{1}{\sqrt{2}} (|00\rangle + |11\rangle)$
I can't think of a better method than shifting all the elements to one side, determining their eigenvalues and finding conditions for which they will remain non-negative. Needless to say this is extremely intensive.
