# Incorporating a Max in optimization objective

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cchen 2016 年 11 月 30 日

I'm trying to use intlinprog to solve a mixed integer linear program where the objective function has a max function embedded in it. For example, the objective may be of the form:
5*max(10-x, 0)+x
The objective is clearly convex and actually piecewise linear. How can I incorporate this in the form
f'x
so as to be able to use intlinprog?
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cchen 2016 年 12 月 5 日

I see what you are saying. Currently, I'm using cvx to model a larger convex mixed-integer problem, which then calls Mosek. It is slow however, and I was hoping to improve upon this by using a Matlab solver. I thought I could use intlinprog since the cvx input to Mosek is an integer linear program, but reading the model, I cannot fully understand the reformulation.
Oskar Adolfson 2017 年 10 月 12 日
I think it is false to say that a convex function is not linear. A convex function can actually be linear, but it doesn't have to be. Try to verify yourself by testing if y = ax is convex.

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### 回答 (2 件)

Matt J 2017 年 10 月 12 日
Splitting this piecewise linear function into regions where it is a linear function is akin to knowing the minimum solution in the first place, so I don't see what use this has.
Not sure why that approach isn't worth pursuing. For this example, you simply add the constraint x<=10 for the first region and x>=10 for the second.
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Mario CASTRO GAMA 2023 年 10 月 1 日
You can try to use the method presented in this video.

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