Pick optimal combination from matrix
Pick the minimum value of each column and compute the maximum (M) of those.  Althrough there would be other combinations that produce the same maximum value, M cannot be further reduced because any value in M's column would be larger and picking (smaller) values in other columns would not change M which is the smallest in its own column.
If you were looking to minimize the total of these values, then there would be a need for some additional optimization, perhaps using dynamic programming.  As it is, the problem is simple math.
Let's say I have a matrix M which looks like:
[a b c l]
[d e f k]
[g h i o]
I have to pick one element from every column such that I can minimise the maximum value of all those elements.
For eg. If I pick a,e,i,k my answer would be max(a,e,i,k)
To find the most optimum solution, is there any approach which is better than O(n^3)?
I would appreciate some sort of pseudocode/snippet of code if possible.