Handling of decision variable with negative bound in YALMIP

[JackJack]

Dear Professor Johan Löfberg,

I am writing to seek your guidance regarding YALMIP's handling of decision variables with negative bounds, as I've encountered this situation in my optimization problem.

For example

I have implemented a change of variables in my optimization problem, introducing a new decision variable t_8, which is a linear combination of three existing decision variables (x, y, z) and a constant - 2:

Based on the upper and lower bounds of x, y, and z, I have determined that:

• Maximum value of t_8 is 0, occurring when (x, y, z) = (0, 1, 1)
• Minimum value of t_8 is -3, occurring when (x, y, z) = (1, 0, 0)

  I am concerned about how YALMIP processes decision variables with negative lower bounds. Specifically, I would like to understand the internal handling mechanisms when a variable like t_8 has a range from -3 to 0, rather than being strictly non-negative.  

Could you please explain how YALMIP manages variables with negative bounds in its solver interface? I want to ensure that my problem formulation is being interpreted correctly by the solver.

Thank you very much for your time and expertise.

[Johan Löfberg]

yalmip does not handle negative bounds in any way different from any other bound, or absence of bound

[JackJack]

So what does it do in this case ?  I am not sure if my memory is correct but since LP, SOCP, SDP always require non negative decision variable does yalmip come up with a way to by pass the requirement of the solver ?

[Johan Löfberg]

Modern solvers don't have such silly limitations, and if they have that's what you have the modelling language for

[JackJack]

Thank you ! So it automatically handle case like this right ?

[Johan Löfberg]

I don't know what you mean with cases like this, as I don't see anything particular in your model, an equality and a bunch of bounds.