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 $d^*\gt -\infty$