I directly use the min in my code, the error is Invalid constraint: {concave} <= {real constant};

It is unclear what is variables and parameters.

Assume x is a variable then you can write

b+min(1,a)*x<=x

as

t=min(1,a) (t is parameter)

b+t*x<=x

Sometimes you have to adapt the model on paper a little bit to make it easier for Cvx to digest.

sorry, and let me be clear, the b and a are variables, they are both continuous variables greater than 0 and less than 1, and M,K are constant

Your model is not convex then. If you replace min by max it world be ok.

Thanks for your answer, then can I introduce slack variables let min(1,a)>= c and b+c<=1 to solve this problem?

You’d need to introduce binary variables to handle non-convex usage of `min`

. If you search on the internet, you’ll see howto do that. Fro instance, https://yalmip.github.io/tutorial/logicprogramming .

I have browsed the content in the link and have a preliminary study. Thank you for sharing.