Originally posted by: Marjoo

Hi everyone. I hope this is the right forum to ask this question.

I have a minimisation problem with two conflicting objectives, which both have a weight. For simplicity lets consider the objective: minimisation (weight (sum over max{0, value1-value2}) + (1-weight) sum value2) subject to several constraints.

Hence, if value2 exceeds value1, the first part should be zero. Otherwise, it should be equal to value1-value2. To force this, the optimisation problem is rewritten as: minimisation (weight (sum over variable) + (1-weight) sum value2), subject to variable >= value1-value2, variable >=0. Hence, the variable is either be zero or has the positive value value1-value2.

However, now I want to make a maximisation problem out of this. Simply minimising the negative objective results in an unbounded solutions, as the variable can increase as much as it wants. How can I again assure that if value2 exceeds value1, the first part is zero; otherwise, it should be equal (so not greater than!) to value1-value2?

Thanks in advance!

Does this help? LPs and the Positive Part

Originally posted by: Marjoo

Thank you, I believe that this indeed made me rewrite it. However, now I do have a non-linear problem, and I'll have to see if that will be a problem.

Nevertheless, thank you!