how to deal with sum of square root in gurobi?

[Quincy]

Hi, I am a beginner in optimization and gurobi.

A few days ago, I read a paper which is written by a Ph.D. candidate, it has a constraint I have never seen before, and I could not realize it.

after simplified:

(1)

in which P and Q are variables, c is a constant.

it's the sum of sqrts, then he transferred (1) into standard SOC

            (2)

he realized it with CVX and Gurobi

I am wondering how could he make it?

I spend a few days but failed, once have a problem with sqrt, most of the post use piece-wise linear to approximate, but it so complicated, so how to deal with sum of sqrt in gurobi?

[Dr Michael F]

Hi Quincy.

SOC constraints are a little tricky the first time you use them.  Add auxiliary variables y_i and then add the second order cone constraints:

P_i^2+Q_i^2 <= y_i^2

and the linear constraint:

sum(y_i) <= c

Regards,

Michael 

[Quincy]

Hi Micheal, 

thank u so much for your help.

I have another question. If I have a constraint which is

P^2+Q^2=U^2*I^2    (1)

I_1 + I_2 <= C          (2)

where P/Q/U/I are variables, and C is constant.

I convert (1) into a rotate SOC form:

P^2+Q^2<=u*i

where u=U^2, i = I^2

so how to deal with (2)?

could I add constraints like this is available?

U^2<=u

I^2<=i

thank u again

best regards

在 2018年4月3日星期二 UTC+8下午5:53:54，Dr Michael F写道：