How to write the constraint involving indicator functions in CVX?

MIDCP
1

How to write the following constraints involving indicator functions in CVX?

0 \leq \sum_{i=1}^{m} \omega_{i} \cdot \mathbb{1}_{\{x > D_{i}\}} \leq 1, \forall x \in R,

and

0 \leq \sum_{i=1}^{m} \omega_{i} \cdot \mathbb{1}_{\{ D_{i} < x \leq M_{i}\}} \leq 1, \forall x \in R

where, D and M are given, while \omega is the decision variable.

Thank you for your time.

2

The concept of indicator constraints is not available in Cvx. You must convert the problem to an ordinary MIP. This often involves using a so-called Big-M formulation

1 Like
3

It is not clear to me what the constraints are, in particular, what x is.

If x is a CVX (decision) variable or expression, you will have to use Big M, as @Erling suggested. if x is input data (a regular MATLAB variable), then Big M is not necessary, but then the way the constraint is written doesn’t seem to make sense.

Sp please clarify.

4

Thank you very much for your reply.

5

Thank you so much for your reply. It was a mistake.