Check SCS performance on QETAMACR

[stephane-caron]

The conversion of SCS problems may be slightly suboptimal, see #19 (comment)

For instance on QETAMACR:

 - Solving QETAMACR with solver SCS-3.0
 - Optimal objective 86760.37
------------------------------------------------------------------
               SCS v3.2.1 - Splitting Conic Solver
        (c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem:  variables n: 688, constraints m: 1089
cones:    z: primal zero / dual free vars: 354
          b: box cone vars: 735
settings: eps_abs: 1.0e-04, eps_rel: 1.0e-04, eps_infeas: 1.0e-18
          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): 3097, nnz(P): 4447
------------------------------------------------------------------
 iter | pri res | dua res |   gap   |   obj   |  scale  | time (s)
------------------------------------------------------------------
     0| 9.63e+02  7.80e+02  1.31e+04 -1.03e+04  1.00e-01  5.59e-03
   250| 3.88e+00  2.41e+01  1.46e+03  3.75e+04  1.39e+01  3.98e-02
   500| 1.81e+00  1.24e+00  7.27e+01  4.78e+04  1.39e+01  6.88e-02
   750| 4.44e+03  8.37e+03  4.17e+04  4.78e+04  1.39e+01  9.75e-02
  1000| 1.76e+00  9.52e-01  5.90e+01  5.07e+04  1.39e+01  1.26e-01
  1250| 2.05e+00  1.25e+00  6.91e+01  5.19e+04  1.39e+01  1.55e-01
  1500| 2.38e+00  1.46e+00  8.32e+01  5.32e+04  1.39e+01  1.85e-01
  1750| 2.78e+00  1.62e+00  9.37e+01  5.47e+04  1.39e+01  2.14e-01
  2000| 3.19e+00  1.83e+00  1.07e+02  5.64e+04  1.39e+01  2.43e-01
  2250| 3.28e+00  2.08e+00  1.12e+02  5.82e+04  1.39e+01  2.71e-01
  2500| 3.57e+00  2.20e+00  1.21e+02  6.02e+04  1.39e+01  3.00e-01
  2750| 4.01e+00  2.46e+00  1.32e+02  6.25e+04  1.39e+01  3.29e-01
  3000| 4.56e+00  2.79e+00  1.48e+02  6.53e+04  1.39e+01  3.58e-01
  3250| 5.17e+00  2.97e+00  1.64e+02  6.88e+04  1.39e+01  3.88e-01
  3500| 8.03e+03  1.09e+05  7.06e+04 -5.43e+03  1.39e+01  4.1(2 res
  3750| 3.65e+00  3.11e+00  1.01e+02  7.74e+04  1.39e+01  4.51e-01
  4000| 3.02e+00  1.65e+00  7.21e+01  7.92e+04  1.39e+01  4.80e-01
  4250| 2.95e+00  1.48e+00  6.84e+01  8.08e+04  1.39e+01  5.08e-01
  4500| 3.02e+00  1.47e+00  6.86e+01  8.25e+04  1.39e+01  5.38e-01
  4750| 6.91e-01  1.08e+00  1.32e+01  8.37e+04  1.39e+01  5.67e-01
  5000| 3.15e-01  5.24e-01  7.56e+00  8.39e+04  1.39e+01  5.96e-01
  5250| 3.67e-01  3.13e-01  8.63e+00  8.40e+04  1.39e+01  6.24e-01
  5500| 3.81e-01  2.40e-01  8.38e+00  8.41e+04  1.39e+01  6.53e-01
  5750| 3.80e-01  1.99e-01  8.50e+00  8.42e+04  1.39e+01  6.82e-01
  6000| 3.73e-01  2.01e-01  8.38e+00  8.43e+04  1.39e+01  7.12e-01
  6250| 4.66e+03  6.40e+04  5.01e+03  9.08e+04  1.39e+01  7.42e-01
  6500| 3.15e-01  1.95e-01  7.58e+00  8.46e+04  1.39e+01  7.72e-01
  6750| 3.19e-01  1.89e-01  7.43e+00  8.47e+04  1.39e+01  8.00e-01
  7000| 3.30e-01  1.94e-01  7.62e+00  8.48e+04  1.39e+01  8.29e-01
  7250| 3.41e-01  1.99e-01  7.82e+00  8.49e+04  1.39e+01  8.60e-01
  7500| 3.25e-01  2.19e-01  7.48e+00  8.50e+04  1.39e+01  8.90e-01
  7750| 3.18e-01  2.05e-01  7.33e+00  8.51e+04  1.39e+01  9.18e-01
  8000| 3.12e-01  2.06e-01  7.18e+00  8.51e+04  1.39e+01  9.50e-01
  8250| 3.05e-01  1.98e-01  7.05e+00  8.52e+04  1.39e+01  9.78e-01
  8500| 3.02e-01  1.93e-01  6.99e+00  8.53e+04  1.39e+01  1.01e+00
  8750| 3.02e-01  3.85e-01  6.97e+00  8.54e+04  1.39e+01  1.04e+00
  9000| 5.96e+02  8.19e+03  1.18e+03  8.79e+04  1.39e+01  1.06e+00
  9250| 2.57e-01  1.97e-01  5.87e+00  8.56e+04  1.39e+01  1.09e+00
  9500| 2.37e-01  1.72e-01  5.53e+00  8.56e+04  1.39e+01  1.12e+00
  9750| 2.21e-01  1.60e-01  5.25e+00  8.57e+04  1.39e+01  1.15e+00
 10000| 2.08e-01  1.53e-01  5.01e+00  8.58e+04  1.39e+01  1.18e+00
 10250| 1.94e-01  1.42e-01  4.72e+00  8.58e+04  1.39e+01  1.21e+00
 10500| 1.80e-01  1.38e-01  4.33e+00  8.59e+04  1.39e+01  1.24e+00
 10750| 1.71e-01  3.28e-01  4.34e+00  8.59e+04  1.39e+01  1.26e+00
 11000| 1.45e-01  1.26e-01  3.62e+00  8.60e+04  1.39e+01  1.29e+00
 11250| 1.27e-01  1.09e-01  3.35e+00  8.60e+04  1.39e+01  1.32e+00
 11500| 1.13e-01  1.02e-01  3.07e+00  8.60e+04  1.39e+01  1.35e+00
 11750| 8.21e+02  3.67e+04  1.51e+03  9.01e+04  1.39e+01  1.38e+00
 12000| 8.79e-02  1.41e-01  2.65e+00  8.61e+04  1.39e+01  1.41e+00
 12225| 7.25e-02  8.49e-02  2.35e+00  8.61e+04  1.39e+01  1.43e+00
------------------------------------------------------------------
status:  solved
timings: total: 1.43e+00s = setup: 5.27e-03s + solve: 1.43e+00s
         lin-sys: 1.30e+00s, cones: 6.17e-02s, accel: 1.50e-02s
------------------------------------------------------------------
objective = 86139.626049
------------------------------------------------------------------