I am solving a LP model using Benders decomposition. The subproblem is a LP with piecewise linear objective. I am a bit puzzled at what the objective function of the dual of the subproblem is. I have tried the standard way of expressing the objective function as a weighted sum of the dual variables multiplied by their curresponding RHS, however, this way of calculating the dual objective value does not seem to be correct when the variable with the piecewise linear objective is beyond the first linear segment.
I am aware that I can retrieve the subproblem objective value by calling
but I need the expression of the dual objective function for Benders optimality cut. How can we find a valid Benders cut with piecewise linear subproblem?
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