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Given $0 < w \leq 1$, I would like to use the function: $$ -\ln(1 - w \sigma(t)), $$ where $\sigma(t) = 1 / (1 + \exp(-t))$ is the sigmoid function, in my objective. It's a bit tedious, but this function is convex. But I was not able to find any DCP representation of this function so that I can incorporate it into CVXPY. Note, that when $w = 1$ this is the loss function of a negative event in logistic regression, so the case of $w = 1$ is easy.

Update My bad.. it is not convex, as pointed out in one of the answers.

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It doesn't look particularly convex: https://www.desmos.com/calculator/v17plvovb8.

enter image description here

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    $\begingroup$ My bad... indeed it is not. Going to look for the mistake. $\endgroup$
    – Alex Shtoff
    Commented Jun 17 at 13:23

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