Incorporating a Max in optimization objective

Question

cchen 2016-11-30

1
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/314746-incorporating-a-max-in-optimization-objective

回答： Mario CASTRO GAMA 2023-10-1

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?

3 个评论
显示 1更早的评论隐藏 1更早的评论

cchen 2016-12-5

编辑：cchen 2016-12-5

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 2017-10-12

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.

请先登录，再进行评论。

请先登录，再回答此问题。

Answer 1

Matt J 2017-10-12

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/314746-incorporating-a-max-in-optimization-objective#answer_285392

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.