How to check the convexity of the objective function?

17 次查看（过去 30 天）

Alexa 2024-5-21

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2120821-how-to-check-the-convexity-of-the-objective-function

评论： Alexa 2024-5-21

Hi Everyone, I have the following objective function: Max 1-exp(- SNR_threshold/average SNR) and subject to power constraints,0>p< P_max. How can I check if it convex problem or not?

0 个评论
显示 -2更早的评论隐藏 -2更早的评论

请先登录，再进行评论。

请先登录，再回答此问题。

回答（1 个）

Kunal Kandhari 2024-5-21

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/2120821-how-to-check-the-convexity-of-the-objective-function#answer_1460666

Hi Alexa,

Since, If the second derivative of a function is always positive or non-negative over an interval, then the function is convex over that interval so you can use the "diff" function in MATLAB to calculate the derivatives and check if f'' >= 0

You can read about the usage of "diff" function from the following documentation:

https://in.mathworks.com/help/matlab/ref/diff.html

7 个评论
显示 5更早的评论隐藏 5更早的评论

Torsten 2024-5-21

在 MATLAB Online 中打开

I don't understand the variables you try to optimize and I don't understand your constraints.

If you wrote

max(1-exp(-x))

under the constraint

0 <= x <= P_max

I'd immediately say: x = P_max is the solution.

But I can't tell what is hidden behind your problem formulation

Max (1-exp(- SNR_threshold/average SNR))

subject to power constraints,

0>p< P_max

Alexa 2024-5-21

@Torsten

Okay, thank you. I am trying to maximize the probability that the SNR is greater than the SNR threshold, and my variable is the power allocation(p) and the P_max is the totoal power. This is ((1-exp(- SNR_threshold/average SNR)) ) to find the probability of each SNR.

请先登录，再进行评论。

请先登录，再回答此问题。