Update to v300.200.900, which has USE_SPECTRAL_CONES=1

[odow]

No description provided.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 91.46%. Comparing base (45f1507) to head (b5bc9dd).
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@@            Coverage Diff             @@
##           master     #327      +/-   ##
==========================================
+ Coverage   91.01%   91.46%   +0.45%     
==========================================
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  Lines         601      633      +32     
==========================================
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  Misses         54       54              

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[odow]

So this passes some of the upstream examples: https://github.com/dance858/scs/blob/master/test/spectral_cones_problems/exp_design.h

julia> begin
       A_v = [
           -1.0, 1.0, -1.0, 3.24, 0.16, 1.0, 4.84, 3.61, 1.0, -1.0, 2.54558441,
           -0.11313708, -0.14142136, 1.24450793, 0.26870058, -2.12132034, -1.0,
           2.03646753, 0.05656854, 0.56568542, 0.93338095, 4.03050865, 0.28284271,
           -1.0, 1.0, 0.04, 0.01, 0.16, 0.01, 2.25, -1.0, 1.13137085, -0.02828427,
           -0.05656854, 0.16970563, 0.21213203, -0.42426407, -1.0, 0.64, 0.01, 0.16,
           0.09, 2.25, 0.04, -1.0,
       ]
       A_i = [
           7, 0, 8, 1, 2, 3, 4, 5, 6, 9, 1, 2, 3, 4, 5, 6, 10, 1, 2, 3, 4, 5, 6, 11, 1,
           2, 3, 4, 5, 6, 12, 1, 2, 3, 4, 5, 6, 13, 1, 2, 3, 4, 5, 6, 14,
       ]
       A_p = [0, 1, 3, 10, 17, 24, 31, 38, 45]
       b = [1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0]
       A = SparseMatrixCSC(15, 8, A_p.+1, A_i.+1, A_v)
       end;

julia> using JuMP, SCS

julia> model = Model(SCS.Optimizer)
A JuMP Model
├ solver: SCS
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> @variable(model, x[1:8])
8-element Vector{VariableRef}:
 x[1]
 x[2]
 x[3]
 x[4]
 x[5]
 x[6]
 x[7]
 x[8]

julia> @objective(model, Min, 1.0 * x[1])
x[1]

julia> @constraint(model, b[1:1] - A[1:1, :] * x in Zeros())
[-x[2] + 1] ∈ Zeros()

julia> @constraint(model, b[2:7] - A[2:7, :] * x in Nonnegatives())
[-3.24 x[3] - 2.54558441 x[4] - 2.03646753 x[5] - x[6] - 1.13137085 x[7] - 0.64 x[8] + 1, -0.16 x[3] + 0.11313708 x[4] - 0.05656854 x[5] - 0.04 x[6] + 0.02828427 x[7] - 0.01 x[8] + 1, -x[3] + 0.14142136 x[4] - 0.56568542 x[5] - 0.01 x[6] + 0.05656854 x[7] - 0.16 x[8] + 1, -4.84 x[3] - 1.24450793 x[4] - 0.93338095 x[5] - 0.16 x[6] - 0.16970563 x[7] - 0.09 x[8] + 1, -3.61 x[3] - 0.26870058 x[4] - 4.03050865 x[5] - 0.01 x[6] - 0.21213203 x[7] - 2.25 x[8] + 1, -x[3] + 2.12132034 x[4] - 0.28284271 x[5] - 2.25 x[6] + 0.42426407 x[7] - 0.04 x[8] + 1] ∈ Nonnegatives()

julia> @constraint(model, b[8:end] - A[8:end, :] * x in MOI.LogDetConeTriangle(3))
[x[1], x[2], x[3], x[4], x[5], x[6], x[7], x[8]] ∈ MathOptInterface.LogDetConeTriangle(3)

julia> optimize!(model)
------------------------------------------------------------------
	       SCS v3.2.9 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 8, constraints m: 15
cones: 	  z: primal zero / dual free vars: 1
	  l: linear vars: 6
	  d: logdet vars: 8, dsize: 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, rho_x: 1.00e-06
	  acceleration_lookback: 10, acceleration_interval: 10
	  compiled with openmp parallelization enabled
lin-sys:  sparse-direct-amd-qdldl
	  nnz(A): 45, nnz(P): 0
------------------------------------------------------------------
 iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
     0| 1.06e+01  1.44e+00  1.46e+01 -8.15e+00  1.00e-01  1.22e-04 
   250| 1.82e-04  3.01e-06  1.87e-04  3.03e+00  3.41e-01  7.72e-04 
------------------------------------------------------------------
status:  solved
timings: total: 7.74e-04s = setup: 3.64e-05s + solve: 7.37e-04s
	 lin-sys: 4.86e-05s, cones: 2.37e-04s, accel: 1.10e-05s
------------------------------------------------------------------
objective = 3.033227
------------------------------------------------------------------

julia> opt = 3.0333290743428574
3.0333290743428574

But it fails a bunch of unit tests.

Here's one that it fails. The answer should be t = log(5):

julia> using JuMP, SCS

julia> model = Model(SCS.Optimizer)
A JuMP Model
├ solver: SCS
├ objective_sense: FEASIBILITY_SENSE
├ num_variables: 0
├ num_constraints: 0
└ Names registered in the model: none

julia> @variable(model, t)
t

julia> @objective(model, Max, t)
t

julia> @constraint(model, [t, 1, 3, 2, 2, 1, 1, 3] in MOI.LogDetConeTriangle(3))
[t, 1, 3, 2, 2, 1, 1, 3] ∈ MathOptInterface.LogDetConeTriangle(3)

julia> optimize!(model)
------------------------------------------------------------------
	       SCS v3.2.9 - Splitting Conic Solver
	(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 1, constraints m: 8
cones: 	  d: logdet vars: 8, dsize: 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, rho_x: 1.00e-06
	  acceleration_lookback: 10, acceleration_interval: 10
	  compiled with openmp parallelization enabled
lin-sys:  sparse-direct-amd-qdldl
	  nnz(A): 1, nnz(P): 0
------------------------------------------------------------------
 iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
     0| 3.00e+00  1.00e+00  2.50e+00 -1.25e+00  1.00e-01  2.38e-04 
    25| 1.90e+06  0.00e+00  2.51e+19 -1.32e+19  1.00e-01  3.58e-04 
------------------------------------------------------------------
status:  unbounded
timings: total: 3.62e-04s = setup: 6.72e-05s + solve: 2.95e-04s
	 lin-sys: 4.54e-06s, cones: 8.57e-05s, accel: 7.04e-07s
------------------------------------------------------------------
objective = -inf
------------------------------------------------------------------

[araujoms]

I would expect the vectorization to be the same as the one in the PSD cone, which is not the same as the MOI one, so you need a bridge.

[odow]

I thought so too, but the experiment design example worked

[araujoms]

Just tried the example, and it works if you minimise instead of maximising, and the answer is correct if you use the SCS vectorization instead of the MOI one. No idea why the example worked, perhaps the matrix is by coincidence the same in both vectorizations?

Looks like they implemented the cone t >= - u logdet(X/u) instead of the more standard t <= u logdet(X/u).

julia> scsmat(v) = Hermitian([v[1] v[2]/sqrt(2) v[3]/sqrt(2); 0 v[4] v[5]/sqrt(2);0 0 v[6]])
scsmat (generic function with 1 method)

julia> v = [3, 2, 2, 1, 1, 3];

julia> logdet(scsmat(v))
0.8451929858692304

[odow]

A bridge it is then

[dance858]

You're right, we use a different convention for the log-determinant cone. Sorry for that; I should have told you earlier.

I wrote down the cone definitions we used in #316.

[odow]

It's times like this when I really appreciate the bridge system in MOI. A set that's scaled, pemuated, and the first element negated? Not a problem.

[odow]

Going to merge this as-is.

Adding NormNuclearCone is going to require a change to MathOptInterface.

(Not for any technical cone/SCS reason, just so that we can keep using the existing utility functions for manipulating the constraint matrix; we assume that all cones have a unique representation for a given dimension, which isn't the case for the NormNuclearCone and NormSpectralCone.)