# Solving SDP problem is 100x slower than Matlab CVX

**URL:** <https://discourse.julialang.org/t/solving-sdp-problem-is-100x-slower-than-matlab-cvx/79704>\
**Category:** Optimization (Mathematical)\
**Tags:** convex-optimization\
**Created:** [April 19, 2022, 7:31pm UTC](https://discourse.julialang.org/t/solving-sdp-problem-is-100x-slower-than-matlab-cvx/79704 "2022-04-19T19:31:36Z")\
**Posts on this page:** 1\
**Showing post:** 5

<div class="post-metadata">

**Author:** ![biona001](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/biona001/32/16497_2.png) [@biona001](https://discourse.julialang.org/u/biona001)\
**Post date:** [April 19, 2022, 9:03pm UTC](https://discourse.julialang.org/t/solving-sdp-problem-is-100x-slower-than-matlab-cvx/79704/5 "2022-04-19T21:03:48Z")

</div>

On my mac, `Hypatia.jl` code above solves the original problem in ~3 seconds which is good enough for my purposes. Thank you very much!

For the approach using `Dualization.jl`, I’m getting roughly 9 seconds, but it seems to be solving to greater accuracy than Matlab’s CVX.

```julia
function julia_dual(Sigma::Matrix)
    p = size(Sigma, 1)
    svar = Variable(p)
    problem = maximize(sum(svar), svar ≥ 0, 1 ≥ svar, 2*Sigma - Diagonal(svar) == Semidefinite(p))
    solve!(problem, Dualization.dual_optimizer(SCS.Optimizer))
    return evaluate(svar)
end
@time s_dual = julia_dual(Sigma) # compile
@time s_dual = julia_dual(Sigma)

  9.215603 seconds (2.61 M allocations: 222.878 MiB, 0.49% gc time, 0.32% compilation time)
 11.798738 seconds (2.53 M allocations: 218.782 MiB, 0.38% gc time)
------------------------------------------------------------------
	       SCS v3.0.0 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem: variables n: 80401, constraints m: 60701
cones: z: primal zero / dual free vars: 40201
	  l: linear vars: 400
	  s: psd vars: 20100, ssize: 1
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, warm_start: 0
	  acceleration_lookback: 10, acceleration_interval: 10
lin-sys: sparse-direct
	  nnz(A): 121201, nnz(P): 0
------------------------------------------------------------------
 iter | pri res | dua res | gap | obj | scale | time (s)
------------------------------------------------------------------
     0| 2.25e+01 2.00e+00 1.50e+04 -7.12e+03 1.00e-01 2.68e-02 
   250| 4.05e-03 2.54e-04 1.95e-02 1.73e+02 1.00e-01 4.25e+00 
   475| 1.72e-04 2.62e-04 8.63e-03 1.72e+02 1.02e+00 8.69e+00 
------------------------------------------------------------------
status: solved
timings: total: 8.82e+00s = setup: 1.28e-01s + solve: 8.69e+00s
	 lin-sys: 1.07e+00s, cones: 7.06e+00s, accel: 8.35e-02s
------------------------------------------------------------------
objective = 172.107787
------------------------------------------------------------------
------------------------------------------------------------------
	       SCS v3.0.0 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem: variables n: 80401, constraints m: 60701
cones: z: primal zero / dual free vars: 40201
	  l: linear vars: 400
	  s: psd vars: 20100, ssize: 1
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, warm_start: 0
	  acceleration_lookback: 10, acceleration_interval: 10
lin-sys: sparse-direct
	  nnz(A): 121201, nnz(P): 0
------------------------------------------------------------------
 iter | pri res | dua res | gap | obj | scale | time (s)
------------------------------------------------------------------
     0| 2.25e+01 2.00e+00 1.50e+04 -7.12e+03 1.00e-01 3.85e-02 
   250| 4.05e-03 2.54e-04 1.95e-02 1.73e+02 1.00e-01 5.77e+00 
   475| 1.72e-04 2.62e-04 8.63e-03 1.72e+02 1.02e+00 1.11e+01 
------------------------------------------------------------------
status: solved
timings: total: 1.13e+01s = setup: 1.88e-01s + solve: 1.11e+01s
	 lin-sys: 1.38e+00s, cones: 9.03e+00s, accel: 1.04e-01s
------------------------------------------------------------------
objective = 172.107787
------------------------------------------------------------------

```

I will try to see how to adjust convergence tolerance

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