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If I have a vector of M "continuous" decision variables (say it is called x) , and if I want a constraint to express that only one of them is allowed to have a nonzero value (i.e. no more than one variable can be nonzero). How can I express such constraint?

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I am not sure if this is going to work as you want -because there is very little information in your question-. But you can introduce a vector of binary variables $w\in\{0,1\}^n$, then add $x_i = w_i\times b_i$ -where $b_i$ is a real number-, and $\sum_i w_i = 1$ (summation in the classical sense not XOR, e.g. $1+1=2$) as constraints. The second condition enforces that only one $w_i$ is $1$ (say $i=j$) and the first condition enforces that only $x_j$ is nonzero and it is equal to $b_j$.

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