# Pick out two related elements from a list using criterion

Suppose I have a list:

$$lst= \{\{k_1, g_1\},\{k_2,g_2\},...,\{k_{max},g_{max}\},...,\{k_n,g_n\}\}$$

Here $$\{k_{max},g_{max}\}$$ is a special element, in which $$g_{max}$$ is the maximum of all $$g_{i}$$

I can use Ordering to find the ordering that sorts the list with respect to the second element of it sublist:

lst[[Ordering[lst[[All, 2]]]]];

then pick out the list having $$g_{max}$$ with lst[[Ordering[lst[[All, 2]]]]][[-1]].

My question is how to pick out a more special list $$\{k^\ast, g^\ast \}$$, for example, having $$g^\ast$$ such that $${\rm{Abs}}[g^\ast] = 50 g_{max}$$? In a real case, the equal sign may not hold exactly. In this case, I still want to find the list, which fits the relation best. It means that to find a list such that $${\rm{Abs}}[g^\ast]$$ is most close to $$50 g_{max}$$ Here is a sample list for your experiment. Thank you very much.

You can try Nearest:
gmax = lst[[Ordering[lst[[All, 2]], -1]]][[1, -1]];