I am trying to understand what an objective function really is. Every sequence alignment method should have an objective function. When it comes to the needleman-wunsch algorithm, what is precisely the objective function? I know there is a dynamic-programming matrix that should be filled. At each cell (i,j) in the matrix, the value is the maximum of three things: value in cell (i,j-1) - gap penalty, value in cell (i-1,j) -gap penalty, value in cell (i-1,j-1)+substitution score. Is this what is called the objective function ?
I would consider the objective function to be the resulting scores of the paths through the dynamic-programming matrix. This is what's actually being optimized, after all. That also nicely matches the definition of an objective function, since each path score represents multiple comparison events summarized in a single real value.