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How to check the convexity of the objective function?

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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?

Answers (1)

Kunal Kandhari
Kunal Kandhari on 21 May 2024
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:
  7 Comments
Torsten
Torsten on 21 May 2024
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
Alexa on 21 May 2024
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.

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