# add second order cone type constraint
**URL:** https://discourse.julialang.org/t/add-second-order-cone-type-constraint/18742
**Category:** Optimization (Mathematical)
**Created:** [December 17, 2018, 1:49pm UTC](https://discourse.julialang.org/t/add-second-order-cone-type-constraint/18742 "2018-12-17T13:49:22Z")
**Posts on this page:** 5
**Page:** 1
### Author:  [@WangQuanmeng](https://discourse.julialang.org/u/WangQuanmeng)
#### Post date: [December 17, 2018, 1:49pm UTC](https://discourse.julialang.org/t/add-second-order-cone-type-constraint/18742/1 "2018-12-17T13:49:22Z")
Hi,
I am new to Julia and JuMP, and I am learning to solve SOCP with integer constraint.
The only example I can find online shows I should add the constraint in the following way.
`@constraint(m, norm(2x[i] - i for i=1:n if c[i] == 1) <= 1)`
Is there a way to call `norm` function with out a looping of iterator with in it ? For example, in my problem, a segment of code would be
```julia
for t in 1:n
for i in 0:t
for j in ( t + 1 ):( n + 1 )
# add socp constraint here
@constraint( model , dd[k , i , j , t , 1] == sqrt( generationCostA( k , t ) ) * x[k , i , j , t] )
@constraint( model , dd[k , i , j , t , 2] == 0.5 * ( d[k , i , j , t] - y[k , i , j] ) )
@constraint( model , norm( dd[k , i , j , t , kk] for kk in 1:2 ) <= 0.5 * ( y[k , i , j] + d[k , i , j , t] ) )
end
end
end
```
the vector within `norm` function has dimension 2. I tried to use `norm([x , y])` , but it does not work. So I have to create dummy variables `dd` , and then I can use iterator within `norm` function.
Can I do it without introduce the dummy variables? Thanks for your time of reading, and much appreciated if you can help me on this!
Qm
---
### Author:  [@miles.lubin](https://discourse.julialang.org/u/miles.lubin)
#### Post date: [December 17, 2018, 3:48pm UTC](https://discourse.julialang.org/t/add-second-order-cone-type-constraint/18742/2 "2018-12-17T15:48:40Z")
> [@WangQuanmeng](#):
>
> I am new to Julia and JuMP
Welcome 🙂
> [@WangQuanmeng](#):
>
> I tried to use `norm([x , y])` , but it does not work.
What doesn’t work? Maybe this should’ve been `norm([x ; y])`? It’s hard to say more without seeing code that reproduces the issue.
---
### Author:  [@WangQuanmeng](https://discourse.julialang.org/u/WangQuanmeng)
#### Post date: [December 18, 2018, 3:16am UTC](https://discourse.julialang.org/t/add-second-order-cone-type-constraint/18742/3 "2018-12-18T03:16:17Z")
Hi,
Thanks for your reply!
When I add constraint in the way of calling `norm( [x , y] )` like the following
```julia
@constraint( model , norm( [sqrt( generationCostA( k , t ) ) * x[ k , i , j , t] , 0.5 * ( d[k , i , j , t] - y[k , i , j] ) ] ) <= 0.5 * ( y[k , i , j] + d[k , i , j , t] ) )
```
the error says `norm` not defined
```julia
ERROR: LoadError: UndefVarError: norm not defined
Stacktrace:
[1] macro expansion at C:\Users\tommyricardo\.julia\packages\JuMP\PbnIJ\src\macros.jl:492 [inlined]
[2] macro expansion at C:\Users\tommyricardo\.julia\packages\JuMP\PbnIJ\src\macros.jl:493 [inlined]
[3] top-level scope at F:\a__top_secret\multiple_units_quadratic.jl:166 [inlined]
[4] top-level scope at .\none:0
in expression starting at F:\a__top_secret\multiple_units_quadratic.jl:161
```
same thing happens if I called `norm( [x ; y] )` `norm( x , y )` or `norm( x ; y )`
```julia
@constraint( model , norm( [sqrt( generationCostA( k , t ) ) * x[ k , i , j , t] ; 0.5 * ( d[k , i , j , t] - y[k , i , j] ) ] ) <= 0.5 * ( y[k , i , j] + d[k , i , j , t] ) )
```
```julia
ERROR: LoadError: UndefVarError: norm not defined
Stacktrace:
[1] macro expansion at C:\Users\tommyricardo\.julia\packages\JuMP\PbnIJ\src\macros.jl:492 [inlined]
[2] macro expansion at C:\Users\tommyricardo\.julia\packages\JuMP\PbnIJ\src\macros.jl:493 [inlined]
[3] top-level scope at F:\a__top_secret\multiple_units_quadratic.jl:166 [inlined]
[4] top-level scope at .\none:0
in expression starting at F:\a__top_secret\multiple_units_quadratic.jl:161
```
It only works if I defined new variables `dd` to make a copy of `x,y` and call `norm( dd[i] for i in 1:2 )`.
```julia
@constraint( model , dd[k , i , j , t , 1] == sqrt( generationCostA( k , t ) ) * x[k , i , j , t] )
@constraint( model , dd[k , i , j , t , 2] == 0.5 * ( d[k , i , j , t] - y[k , i , j] ) )
@constraint( model , norm( dd[k , i , j , t , kk] for kk in 1:2 ) <= 0.5 * ( y[k , i , j] + d[k , i , j , t] ) )
```
But in this way, I have to create a lot of dummy variables `dd`. So I am just wondering if there is a way to call `norm` for adding the constraint without doing a loop?
I did not put all the codes because it is a bit long. But I think this is the part that produce the error, if you need to see the other part as well, please let me know.
Thanks again for your help.
Qm
---
### Author:  [@blegat](https://discourse.julialang.org/u/blegat)
#### Post date: [December 18, 2018, 12:23pm UTC](https://discourse.julialang.org/t/add-second-order-cone-type-constraint/18742/4 "2018-12-18T12:23:21Z")
You need to do `using LinearAlgebra` for `norm` to be available.
---
### Author:  [@WangQuanmeng](https://discourse.julialang.org/u/WangQuanmeng)
#### Post date: [December 19, 2018, 2:28am UTC](https://discourse.julialang.org/t/add-second-order-cone-type-constraint/18742/5 "2018-12-19T02:28:39Z")
Thanks! It works after I add `LinearAlgebra` packages.