How to express I2=log(sum(inv_pos()))

1

Hello, everyone! How can I express I2 ?
Constraint: I1 - I2-r0>=C0
r0 and C0 are both real value. sk(1,N) is variable.

for i=1:N
a(i)=sum_square(y-w(:,i))
end
I1= -sum(a);

Thank you for your attention very much!

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2

Doesn’t your previous topic Log-sum-inv，is it right address this?

3

Yes, I have deduced Log-sum-inv. But it is complicated， is there a simpler expression ?

4

The two formulations I know of are provided in section 5.2.7 Log-sum-inv of https://docs.mosek.com/modeling-cookbook/expo.html#modeling-with-the-exponential-cone

5

That’s all right, thank you Mark!

6

@Shuzhen Sorry for bothering. May I know how you express your formula later? I have the same formula but can’t express it. Thanks.

7

@Ben Have you read How to express log(1+ sum ( 1./x ) ) in CVX? - #2 by Mark_L_Stone and the Mosek Modeling Cookbook section on log-sum-inv to which it refers?

if that doesn’t suffice, please show your mathematical problem formulation, and indicate what you are having trouble with,

8

I have tried to express it with Log_sum_inv, but I don’t know if it is right as we not do the work latter.

9

@Shuzhen Can I have a look at your code as a reference, thanks a lot!!!

10 
variable yi(1,K)
variable sk(1,K)
for i=1:8 
    skk(i)=power(norm(y_f-w(:,i)),2)+2*(y_f-w(:,i))'*(y-y_f)+H_U^2;
end
for i=1:K
    if a_f(i)==1
        xi(i)=1/roll;
        xi(i)>=exp(yi(i));
        for i=1:K
            ex=ex+exp(yi(i));
        end
        for k=1:K
           if(k~=i)
               (H_U^2+sk(i))/(beta_1*pii_f(k))>=exp(-yi(k));
           end
        end
        c>=log(ex);
    end
    sk(i)<=skk(i);
end
11

You should use log_sum_exp