Hello!

I have the following problem:

I want to minimize a least square problem with restrictions using quadratic module from xpress MP. The model has the following form:

F:=sum(i in 1..N) (y(i)-sum(j in 1..3) w(j)*x(j))^2!and restrictionforall(i in 1..3) w(j) is_free!the objectiveminimize(F)

Now, I want to complicate the model. Let T>0 be a threshold which is given as input.

All the absolute differences which are not in the interval [-T,T] introduce the error T^2.

The model become(because I don't have an equation editor I use the mosel syntax):

F:=sum(i in 1..N | abs(y(i)-sum(j in 1..3) x(i)*w(j))<T)) (y(i)-sum(j in 1..3) w(j)*x(j))^2+sum(i in 1..N |abs(y(i)-sum(j in 1..3) x(i)*w(j)>=T)) T^2 minimize(F)

Can be solved with Xpress MP this type of problem?

Hi,

If I read your model correctly then yes, this should be possible.

I would consider a formulation along these lines:

deviation = y(i)-sum(j in 1..3) x(i)*w(j)

deviation <= T + positive_surplus

deviation >= -T - negative_surplus

minimize (positive_surplus^2 + negative_surplus^2 )