# Multi-bound Variable

Hello
I need to define a variable with limited domain in discrete parts in cvx
for example variable x that is bounded like
0 <= x <= 1
10 <= x <= 11
but i cant define like above in cvx.
is it possible to have a variable like that in cvx?

This can be done as MIDCP

RobPratt provides a general formulation at https://math.stackexchange.com/questions/3961000/decision-variable-must-lie-in-union-of-multiple-disjoint-intervals/3961273

variable x
variable z(2) binary
10*z(2) <= x <= z(1) + 11*z(2)
sum(z) == 1

Note: I corrected a typo in the statement which is now variable z(2) binary

but I actually wanted to define a variable with two separate domain so i can simulate binary variable like this:
-1e-6<=x<=1e-6
1-1e-6<=x<=1+1e-6
because I get the error “SDTP3 does not support integer variables.”
if I use:
binary z(2)
I get the same error and It would be useless for me.
what is this error about and is there any other way to define binary variable in SDTP3?

Try other solvers.

# Solvers¶

## Supported solvers¶

This version of CVX supports four solvers, each with different capabilities:

Solver name LP QP SOCP SDP GP Integer
SeDuMi Y Y Y Y E N
SDPT3 Y Y Y Y E N
Gurobi Y Y Y N N Y
MOSEK Y Y Y Y Y Y
GLPK Y N N N N Y

(key: Y = Yes, N = No, E = Experimental)

IT worked
thanks so much