Wrong table about SCS and QP in homepage
xinran1228 opened this issue · comments
Under "Supported Solvers", I think SCS can not support QP.
Please see the SCS reference, https://cran.r-project.org/web/packages/scs/scs.pdf, it is not mentioned that scs can solve QP.
In addition, using SCS in QP will produce incorrect results. For example,
What is the value of res_scs$status?
"optimal"
The issue is likely the termination criterion. Play around with the solver parameters.
PS. I am unlikely to expend any more time on this thread if you continue to post pictures and/or not provide a self-contained reproducible example.
Sorry, I am not very familiar with the process of issues. That's the code.
Please take a look.
To Reproduce
library(PortfolioAnalytics)
library(CVXR)
# load data
data(edhec)
ret_edhec <- tail(edhec, 60)
# CVXR optimization
X <- as.matrix(ret_edhec)
N <- ncol(ret_edhec)
wts <- Variable(N)
sigma_value <- cov(ret_edhec)
obj <- quad_form(wts, sigma_value)
# long_only full_investment portfolio
prob_cvxr <- Problem(Minimize(obj), constraints = list(wts >= 0, sum(wts) == 1))
# SCS problem
res_scs <- CVXR::solve(prob_cvxr, solver = "SCS")
sqrt(res_scs$value)
res_scs$status
res_osqp <- CVXR::solve(prob_cvxr, solver = "OSQP")
sqrt(res_osqp$value)
res_ecos <- CVXR::solve(prob_cvxr, solver = "ECOS")
sqrt(res_ecos$value)
See below. Solvers have different default parameters and termination criteria. These are all discussed in the examples: https://cvxr.rbind.io/cvxr_examples/cvxr_solver-parameters/.
> res_scs <- CVXR::solve(prob_cvxr, solver = "SCS", verbose = TRUE, eps_abs = 1e-6, eps_rel = 1e-6)
------------------------------------------------------------------
SCS v3.0.0 - Splitting Conic Solver
(c) Brendan O'Donoghue, Stanford University, 2012
------------------------------------------------------------------
problem: variables n: 14, constraints m: 29
cones: z: primal zero / dual free vars: 1
l: linear vars: 13
q: soc vars: 15, qsize: 1
settings: eps_abs: 1.0e-06, eps_rel: 1.0e-06, eps_infeas: 1.0e-07
alpha: 1.50, scale: 1.00e-01, adaptive_scale: 1
max_iters: 2500, normalize: 1, warm_start: 0
lin-sys: sparse-direct
nnz(A): 197, nnz(P): 0
------------------------------------------------------------------
iter | pri res | dua res | gap | obj | scale | time (s)
------------------------------------------------------------------
0| 1.04e+00 3.78e-02 3.78e-02 1.89e-02 1.00e-01 1.72e-05
250| 1.02e-05 4.95e-08 9.86e-09 1.03e-05 6.73e-04 3.23e-04
275| 1.76e-06 8.58e-09 1.73e-09 1.03e-05 6.73e-04 3.55e-04
------------------------------------------------------------------
status: solved
timings: total: 4.61e-04s = setup: 1.04e-04s + solve: 3.57e-04s
lin-sys: 2.35e-04s, cones: 2.93e-05s, accel: 0.00e+00s
------------------------------------------------------------------
objective = 0.000010
------------------------------------------------------------------
> sqrt(res_scs$value)
[1] 0.003210955
> res_scs$status
[1] "optimal"
> res_osqp <- CVXR::solve(prob_cvxr, solver = "OSQP", verbose = TRUE, eps_abs = 1e-6, eps_rel = 1e-6)
-----------------------------------------------------------------
OSQP v0.6.0 - Operator Splitting QP Solver
(c) Bartolomeo Stellato, Goran Banjac
University of Oxford - Stanford University 2019
-----------------------------------------------------------------
problem: variables n = 13, constraints m = 14
nnz(P) + nnz(A) = 117
settings: linear system solver = qdldl,
eps_abs = 1.0e-06, eps_rel = 1.0e-06,
eps_prim_inf = 1.0e-04, eps_dual_inf = 1.0e-04,
rho = 1.00e-01 (adaptive),
sigma = 1.00e-06, alpha = 1.60, max_iter = 10000
check_termination: on (interval 25),
scaling: on, scaled_termination: off
warm start: on, polish: on, time_limit: off
iter objective pri res dua res rho time
1 0.0000e+00 1.00e+00 1.00e+02 1.00e-01 4.84e-05s
125 1.0310e-05 5.02e-08 1.11e-12 7.82e-05 1.15e-04s
plsh 1.0310e-05 2.22e-16 3.31e-12 -------- 1.43e-04s
status: solved
solution polish: successful
number of iterations: 125
optimal objective: 0.0000
run time: 1.43e-04s
optimal rho estimate: 1.33e-04
> sqrt(res_osqp$value)
[1] 0.003210968
> res_ecos <- CVXR::solve(prob_cvxr, solver = "ECOS", verbose = TRUE, feas_tol = 1e-6, reltol = 1e-6)
ECOS 2.0.7 - (C) embotech GmbH, Zurich Switzerland, 2012-15. Web: www.embotech.com/ECOS
It pcost dcost gap pres dres k/t mu step sigma IR | BT
0 +0.000e+00 -1.831e-01 +2e+01 7e-01 8e-01 1e+00 1e+00 --- --- 1 1 - | - -
1 +9.353e-04 -1.536e-01 +6e+00 1e-01 1e-01 4e-03 4e-01 0.7220 1e-01 1 1 1 | 0 0
2 +4.421e-04 -6.040e-03 +1e+00 8e-03 3e-02 9e-03 1e-01 0.9890 2e-01 1 1 1 | 0 0
3 +1.855e-04 +2.815e-05 +2e-02 2e-04 9e-04 2e-04 2e-03 0.9785 6e-04 1 1 1 | 0 0
4 +4.881e-05 +2.560e-05 +3e-03 2e-05 1e-04 2e-05 3e-04 0.8755 2e-02 1 1 1 | 0 0
5 +1.494e-05 +3.380e-06 +1e-03 5e-06 4e-05 3e-06 1e-04 0.9218 3e-01 1 1 1 | 0 0
6 +1.289e-05 +9.604e-06 +4e-04 1e-06 1e-05 7e-07 3e-05 0.8102 1e-01 1 1 1 | 0 0
7 +1.095e-05 +1.005e-05 +1e-04 4e-07 3e-06 2e-07 7e-06 0.8434 1e-01 1 1 1 | 0 0
8 +1.072e-05 +1.037e-05 +4e-05 1e-07 1e-06 5e-08 3e-06 0.8880 3e-01 1 1 1 | 0 0
9 +1.032e-05 +1.031e-05 +1e-06 5e-09 4e-08 2e-09 1e-07 0.9669 3e-03 1 1 1 | 0 0
10 +1.031e-05 +1.031e-05 +6e-08 2e-10 2e-09 8e-11 4e-09 0.9591 2e-04 2 1 1 | 0 0
11 +1.031e-05 +1.031e-05 +2e-09 8e-12 8e-11 3e-12 2e-10 0.9769 2e-02 2 1 1 | 0 0
OPTIMAL (within feastol=7.7e-11, reltol=2.2e-04, abstol=2.3e-09).
Runtime: 0.000606 seconds.
> sqrt(res_ecos$value)
[1] 0.00321097
> Got it. It's my fault. Thanks for help.
Your question is perfectly fine and it always helps to have a reproducible example. I am going to close this issue now.