With a non convex nonlinear optimization problem, would specifying the objective function as a sum of absolutes, rather than a sum of differences, make the optimization problem (significantly) more complex?
With my problem, i think working with absolutes rather than sum of squares would be better, if this does not imply a more complex optimization problem
Min X = sum(abs(x1-y1) + abs(x2-y2) + abs(x3-y3)...)
Vs
Min X = sum((x1-y1)^2 + (x2-y2)^2 + (x3-y3)^2...)
Hi, the main difference between your two criteria is that the absolute value is non-differentiable. Thus, you cannot use a nonlinear optimizer that requires differentiability of the objective function and of the constraints (SQP methods in particular).
Impose xi-yi = -epsilon_i and minimize sum(epsilon_1 + epsilon2 +...). This gives the correct infimum for convex problems with absolute value constraints and should give a decent local minimum (at least).
@Richard, does excel solver evolutionary algorithm require differentiability of the objective function and constraints?
I get ok results when i use absolutes with excel solver evolutionary algorithm.
Not sure how valid the results are then, based on whether the mentioned requirement is broken/ violated for solver evolutionary algorithm.
Hi, indeed evolutionary codes are derivative-free so the differentiability of the cost function and constraints is not required. Nevertheless, I am curious to know how the methods takes into accont the constraints.
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