# Duality gap in Convex.jl
**URL:** https://discourse.julialang.org/t/duality-gap-in-convex-jl/93741
**Category:** Optimization (Mathematical)
**Created:** [January 29, 2023, 7:14pm UTC](https://discourse.julialang.org/t/duality-gap-in-convex-jl/93741 "2023-01-29T19:14:53Z")
**Posts on this page:** 3
**Page:** 1
### Author:  [@ajd](https://discourse.julialang.org/u/ajd)
#### Post date: [January 29, 2023, 7:14pm UTC](https://discourse.julialang.org/t/duality-gap-in-convex-jl/93741/1 "2023-01-29T19:14:53Z")
Using the SCS solver with Convex.jl, the output of the solver includes in its printed output the duality gap:
```julia
------------------------------------------------------------------
SCS v3.2.1 - Splitting Conic Solver
(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem: variables n: 2701, constraints m: 7851
cones: z: primal zero / dual free vars: 1
l: linear vars: 50
q: soc vars: 7800, qsize: 2600
settings: eps_abs: 1.0e-04, eps_rel: 1.0e-04, eps_infeas: 1.0e-07
alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1
max_iters: 100000, normalize: 1, rho_x: 1.00e-06
acceleration_lookback: 10, acceleration_interval: 10
lin-sys: sparse-direct-amd-qdldl
nnz(A): 15151, nnz(P): 0
------------------------------------------------------------------
iter | pri res | dua res | gap | obj | scale | time (s)
------------------------------------------------------------------
0| 4.39e+00 1.00e+00 4.96e+01 2.43e+01 1.00e-01 1.02e-02
250| 4.43e-03 7.32e-03 2.04e-01 7.26e+00 1.00e-01 1.34e-01
425| 2.05e-04 1.91e-05 1.42e-04 6.96e+00 3.15e-02 2.24e-01
------------------------------------------------------------------
status: solved
timings: total: 2.24e-01s = setup: 8.90e-03s + solve: 2.15e-01s
lin-sys: 9.77e-02s, cones: 5.55e-02s, accel: 5.25e-03s
------------------------------------------------------------------
objective = 6.961736
------------------------------------------------------------------
```
Is there a simple way to access the final duality gap programmatically using Convex.jl?
---
### Author:  [@ericphanson](https://discourse.julialang.org/u/ericphanson)
#### Post date: [January 29, 2023, 7:43pm UTC](https://discourse.julialang.org/t/duality-gap-in-convex-jl/93741/2 "2023-01-29T19:43:49Z")
You can query the underlying [MathOptInterface](https://jump.dev/MathOptInterface.jl/stable/) model. For example, if we [copy the tutorial example](https://jump.dev/Convex.jl/stable/quick_tutorial/),
> **Tutorial code**
>
> ```julia
> # Make the Convex.jl module available
> using Convex, SCS
>
> # Generate random problem data
> m = 4; n = 5
> A = randn(m, n); b = randn(m, 1)
>
> # Create a (column vector) variable of size n x 1.
> x = Variable(n)
>
> # The problem is to minimize ||Ax - b||^2 subject to x >= 0
> # This can be done by: minimize(objective, constraints)
> problem = minimize(sumsquares(A * x - b), [x >= 0])
>
> # Solve the problem by calling solve!
> solve!(problem, SCS.Optimizer; silent_solver = true)
>
> # Check the status of the problem
> problem.status # :Optimal, :Infeasible, :Unbounded etc.
>
> # Get the optimum value
> problem.optval
>
> ```
We can get the duality gap as:
```julia
julia> import MathOptInterface as MOI
julia> MOI.get(problem.model, MOI.ObjectiveValue()) - MOI.get(problem.model, MOI.DualObjectiveValue())
7.153038624529984e-6
```
---
### Author:  [@ajd](https://discourse.julialang.org/u/ajd)
#### Post date: [January 29, 2023, 7:50pm UTC](https://discourse.julialang.org/t/duality-gap-in-convex-jl/93741/3 "2023-01-29T19:50:31Z")
Thank you! Of course, this is exactly what I need.