How to model affine cone constraint using secondordercone() with coneprog() solver?

Let say I have conic constraint that is translated by a constant, say for example the constant be 1, given by

How to model this constraint using secondordercone() ? I know we can do such constraint using CVX/YALMIP. But I wanted to know is it possible to with coneprog solver.

Answer 1

[Matt J]

Perhaps as follows:

socConstraint.A=blkdiag(A,constant);
socConstraint.b=zeros(n+1,1);
socConstraint.d=[d;0];
socConstraint.gamma=0;

lb=[lb;1]
ub=[ub;1]

[Zakir Hussain Shaik]

Thank you that helped. I realized from your approach that we can also introduce equality constraint on the new slack variable ((n+1)^th term) to be 1.

In the above equation c is any constant.