Slater's condition

If the primal problem is convex i.e. of the form
\begin{align*}
\text{minimize}\quad &f_0(x) \\
    \text{subject to}\quad &f_i(x) \leq 0, \quad i = 1,\cdots,m, \\
                                         &Ax=b
\end{align*} with \(f_0,\cdots,f_m\) convex, and if there exists a point that is strictly feasible, or more precisely an \(x\in \text{relint }\mathcal{D}\) such that

\[ f_i(x) \lt 0, \quad i=1,\cdots,m, \quad Ax=b.\]

Strong duality holds if the above condition is met.
Also, the dual optimum is attained \(d^*\gt -\infty\)