SCS solver presumably failed to find optimum of the problem with CVXPY

[AndreiKeino]

• OS: Windows 7
• SCS Version: SCS v2.1.2
• Compiler: comes with visual studio 2019

Description

SCS solver gives non-optimal result when running in CVXPY for semivariance portfolio optimization task
library pyportfolioopt. I not sure, it is possible that there is the bug in CVXPY somethere.

How to reproduce

file test_efficient_semivariance.py from
https://pyportfolioopt.readthedocs.io/en/latest/
package
function
test_efficient_risk changed for SCS solver to run with

if name == "main":
# from tests.utilities_for_tests import setup_efficient_semivariance, get_data
from utilities_for_tests import setup_efficient_semivariance, get_data
# es = setup_efficient_semivariance()
es = setup_efficient_semivariance(solver='SCS', verbose=True)
w = es.efficient_risk(0.2)

assert isinstance(w, dict)
assert set(w.keys()) == set(es.tickers)
# np.testing.assert_almost_equal(es.weights.sum(), 1)
np.testing.assert_almost_equal(es.weights.sum(), 1, decimal=5)
# assert all([i >= -1e-5 for i in w.values()])
assert all([i >= -1e-4 for i in w.values()])

np.testing.assert_allclose(
    es.portfolio_performance(),
    (0.4567521774612227, 0.2, 2.183678863194344),
    rtol=1e-4,
    atol=1e-4,
)

Output

SCS v2.1.2 - Splitting Conic Solver
(c) Brendan O'Donoghue, Stanford University, 2012

Lin-sys: sparse-direct, nnz in A = 24954
eps = 1.00e-04, alpha = 1.50, max_iters = 5000, normalize = 1, scale = 1.00
acceleration_lookback = 0, rho_x = 1.00e-03
Variables n = 2705, constraints m = 5412
Cones: primal zero / dual free vars: 896
linear vars: 1831
soc vars: 2685, soc blks: 895
WARN: aa_init returned NULL, no acceleration applied.
Setup time: 1.53e-01s

Iter | pri res | dua res | rel gap | pri obj | dua obj | kap/tau | time (s)

 0| 1.29e+21  1.91e+20  9.75e-01 -4.21e+22 -5.39e+20  1.35e+23  1.23e-01 

100| 1.01e-02 9.86e-04 1.03e-01 -9.33e-01 -6.66e-01 2.16e-14 3.13e-01
200| 5.08e-03 4.67e-04 7.16e-02 -7.72e-01 -6.02e-01 2.22e-14 4.86e-01
300| 5.10e-03 1.48e-04 8.54e-02 -7.66e-01 -5.67e-01 2.28e-14 6.81e-01
400| 5.13e-03 5.78e-05 1.01e-01 -7.60e-01 -5.30e-01 2.35e-14 8.51e-01
500| 5.17e-03 2.72e-05 1.17e-01 -7.54e-01 -4.90e-01 2.43e-14 1.02e+00
600| 7.80e-06 1.55e-04 1.32e-06 -4.65e-01 -4.65e-01 1.06e-15 1.21e+00
620| 5.47e-05 6.93e-05 1.85e-06 -4.65e-01 -4.65e-01 2.49e-14 1.25e+00

Status: Solved
Timing: Solve time: 1.25e+00s
Lin-sys: nnz in L factor: 33451, avg solve time: 8.15e-04s
Cones: avg projection time: 1.50e-04s
Acceleration: avg step time: 7.27e-08s

Error metrics:
dist(s, K) = 1.0445e-14, dist(y, K*) = 8.6736e-19, s'y/|s||y| = -6.2081e-17
primal res: |Ax + s - b|_2 / (1 + |b|_2) = 5.4692e-05
dual res: |A'y + c|_2 / (1 + |c|_2) = 6.9337e-05
rel gap: |c'x + b'y| / (1 + |c'x| + |b'y|) = 1.8452e-06

c'x = -0.4650, -b'y = -0.4650

[bodono]

Looks like you want higher accuracy here? If so you can reduce the eps quantity through cvxpy which will yield better solutions (but take more time to solve).

[AndreiKeino]

Thanks, but I am afraid that it's not an accuracy issue. The SCS solver ffound solution which is not exact, the solution is a way too distant and has bigger Sortino ratio - 2.5 times bigger - comparing with one I can get with ECOS solver for that task.