How to SortBy Min[Last]

Question

I have a list of the form

{
{1, {3., ∞, ∞, ∞}},
{2, {1.,1., ∞, ∞}}, 
{3, {0.333333, 0.666667, ∞, ∞}}
}

and I would like to sort it by the minimal of the nested list inside each element, namely, Min[{1.,1., ∞, ∞}] etc. The result should be

{
{3, {0.333333, 0.666667, ∞, ∞}}
{2, {1.,1., ∞, ∞}}, 
{1, {3., ∞, ∞, ∞}},
}

I tried SortBy[x,Min[Last]] but the result is unexpected. Any help?

Answer 1

lst = {{1, {3., ∞, ∞, ∞}}, {2, {1., 1., ∞, ∞}}, {3, {0.333333, 0.666667, ∞, ∞}}};

You can use Min@*Last or Min[Last@#] &

SortBy[Min@*Last]@lst

{{3,{0.333333,0.666667,∞,∞}},{2,{1.,1.,∞,∞}},{1,{3.,∞,∞,∞}}}

or

SortBy[Min[Last@#] &]@lst

{{3,{0.333333,0.666667,∞,∞}},{2,{1.,1.,∞,∞}},{1,{3.,∞,∞,∞}}}