How to add moment constraints in function solvemoment?

[Venkye Zhao]

Dear Johan,

I need your help. 

I knew function mom can add moment constraints in GloptiPoly, such as mom(x^2+y^2) == 2. But I don't know how to add moment constraints in function solvemoment. 

Any comments would be precious for me.

Thanks,

Venkye

[Johan Löfberg]

How is this any different from constraints in the model in general, i.e. x^2+y^2==2

[Venkye Zhao]

Your reply is helpful to me, Thank you very much.

[Venkye Zhao]

Dear Johan,

I need your more help.

I tried the method in your reply, but it didn't work. I will describe my question in detail.

There is a fractional polynomial optimization question to solve

min  p(x) / q(x)

s.t. x \in K,

in which, basic semi-algebra set K = [h(x) == 0, g(x) >= 0], h(x), g(x), p(x) and q(x) are polynomial.

Now, I transform above question to this by the method in this book[1, p150]:

min  p(x)

s.t. x \in K,

     \int_K q(x)d\mu == 1.(moment constraint)

but I don't know how to add the moment constraint \int_K q(x)d\mu == 1 to function solvemoment or other function in YALMIP.

[1] Jean Bernard Lasserre: An Introduction to Polynomial and Semi-Algebraic Optimization. 

https://doi.org/10.1017/CBO9781107447226

Thanks again,

Venkye

[Johan Löfberg]

You cannot do any generalized moments in YALMIP (which I guess that notation is)  To implement it using the standard machinery I guess you would simply introduce a new variable r as objective and the constraint p <= q*r and then proceed as normal

[Venkye Zhao]

Your reply is really helpful, Thank you.