# JuMP & SumOfSquares generate SDPs with ~18x more constraints than YALMIP

**URL:** <https://discourse.julialang.org/t/jump-sumofsquares-generate-sdps-with-18x-more-constraints-than-yalmip/65377>\
**Category:** Optimization (Mathematical)\
**Tags:** jump\
**Created:** [July 27, 2021, 2:19pm UTC](https://discourse.julialang.org/t/jump-sumofsquares-generate-sdps-with-18x-more-constraints-than-yalmip/65377 "2021-07-27T14:19:36Z")\
**Posts on this page:** 1\
**Showing post:** 3

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**Author:** ![ciba12](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/ciba12/32/25211_2.png) [@ciba12](https://discourse.julialang.org/u/ciba12)\
**Post date:** [July 29, 2021, 7:32am UTC](https://discourse.julialang.org/t/jump-sumofsquares-generate-sdps-with-18x-more-constraints-than-yalmip/65377/3 "2021-07-29T07:32:41Z")

</div>

After some playing around I think the problem is due to the norm^2 in the objective function.  
Here are some shorter codes for testing.  
Julia:

```julia
using MosekTools
using JuMP
using DynamicPolynomials
using SumOfSquares
##

n = 100;
model = SOSModel(Mosek.Optimizer)
@variable(model,H[1:n,1:n],PSD); # Matrix parametrizing V
@polyvar(x[1:n]) 
V = x'*H*x;
@constraint(model, V - x'*x >= 0)

@objective(model, Min, sum(H[1:end].^2) ); # slower solve than Yalmip
# @objective(model, Min, sum(H[1:end]) ); # (slightly) faster solve than Yalmip
JuMP.optimize!(model)
@show objective_value(model)

```

Matlab:

```matlab
n = 100;
options = sdpsettings('solver','mosek','sos.newton',0,'sos.congruence',0); % turn off reductions
H = sdpvar(n,n); % Matrix parametrizing V
x = sdpvar(n,1); % State
V = x'*H*x;
con = [sos(V - x'*x), H>=0];

sol = solvesos(con,norm(H(:),2)^2,options,[H(:)]); 
% sol = solvesos(con,sum(H(:)),options,[H(:)]) 

```

On my machine, Mosek takes `12s` to solve the problem from Yalmip and `37s` to solve the JuMP’s problem.

The codes include commented lines with linear objective, to show that the solving speeds (and problem sizes) are almost the same without the norm.

Is there a better way to write the norm^2?

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