Use the solved solution as warm start, why still need 110 iterations to convergence?

[Peargrady]

I use the solved solution as warm start, my code is following:
============================my code========================================
// use result as warm start test
std::vector<c_float> warm_start_x(num_of_knots_ * num_of_variables_per_moment_);
std::vector<c_float> warm_start_y(num_of_knots_ * num_of_variables_per_moment_);
for (int32_t i = 0; i < num_of_knots_ * num_of_variables_per_moment_; ++i)
{
warm_start_x[i] = work->solution->x[i];
warm_start_y[i] = work->solution->y[i];
}
osqp_warm_start(work, CopyData(warm_start_x), CopyData(warm_start_y));
osqp_solve(work);
============================my code========================================

[Peargrady]

I didn't change other settings or data, the result is following:

       OSQP v0.0.0  -  Operator Splitting QP Solver
          (c) Bartolomeo Stellato,  Goran Banjac
    University of Oxford  -  Stanford University 2021

---

problem: variables n = 671, constraints m = 1339
nnz(P) + nnz(A) = 2672
settings: linear system solver = qdldl,
eps_abs = 1.0e-04, eps_rel = 5.0e-04,
eps_prim_inf = 1.0e-04, eps_dual_inf = 1.0e-04,
rho = 1.40e-02 (adaptive),
sigma = 1.00e-06, alpha = 1.60, max_iter = 4000
check_termination: on (interval 10),
time_limit: 5.00e-02 sec,
scaling: on, scaled_termination: off
warm start: on, polish: on, time_limit: 5.00e-02 sec

iter objective pri res dua res rho time
1 -3.7153e+06 3.02e+02 2.11e+03 1.40e-02 6.79e-04s
10 5.6549e+05 8.44e+00 8.10e+02 1.40e-02 8.15e-04s
20 1.7724e+05 3.11e+00 2.38e+02 1.40e-02 1.22e-03s
30 1.0749e+05 1.65e+00 7.30e+01 1.40e-02 1.38e-03s
40 8.0924e+04 2.43e+00 5.82e+01 1.40e-02 1.53e-03s
50 6.7606e+04 2.35e+00 3.38e+01 1.40e-02 1.68e-03s
60 6.4229e+04 1.59e+00 2.17e+01 1.40e-02 1.82e-03s
70 6.4457e+04 1.62e+00 2.17e+01 1.40e-02 1.97e-03s
80 6.5822e+04 6.55e-01 8.54e+00 1.40e-02 2.12e-03s
90 6.6049e+04 2.36e-01 4.56e+00 1.40e-02 2.26e-03s
100 6.5871e+04 1.56e-01 1.82e+00 1.40e-02 2.41e-03s
110 6.5481e+04 9.18e-02 2.16e+00 1.40e-02 2.55e-03s
120 6.5094e+04 8.17e-02 1.91e+00 1.40e-02 2.70e-03s
130 6.4850e+04 6.98e-02 1.38e+00 1.40e-02 2.84e-03s
140 6.4706e+04 5.99e-02 7.87e-01 1.40e-02 2.97e-03s

status: solved
solution polish: unsuccessful
number of iterations: 140
optimal objective: 64706.0039
run time: 3.26e-03s
optimal rho estimate: 8.04e-03

Solve successfully, run time is 0.00326138 number of iterations is 140 rho_estimate is 0.00804216 rho_updates is 0 rho is 0.014
iter objective pri res dua res rho time
1 -3.5634e+06 7.20e+01 4.56e+02 1.40e-02 2.36e-05s
10 4.0694e+05 7.72e+00 3.22e+01 1.40e-02 1.42e-04s
20 4.9752e+04 9.50e-01 2.12e+01 1.40e-02 2.74e-04s
30 5.5393e+04 1.08e+00 1.71e+01 1.40e-02 4.22e-04s
40 6.1027e+04 6.91e-01 1.22e+01 1.40e-02 5.45e-04s
50 6.4330e+04 4.80e-01 1.02e+01 1.40e-02 6.68e-04s
60 6.5418e+04 3.60e-01 6.18e+00 1.40e-02 7.93e-04s
70 6.5655e+04 2.49e-01 2.69e+00 1.40e-02 9.17e-04s
80 6.5472e+04 1.51e-01 1.58e+00 1.40e-02 1.05e-03s
90 6.5174e+04 7.97e-02 1.62e+00 1.40e-02 1.18e-03s
100 6.4919e+04 7.21e-02 1.27e+00 1.40e-02 1.30e-03s
110 6.4759e+04 6.31e-02 8.20e-01 1.40e-02 1.42e-03s

status: solved
solution polish: unsuccessful
number of iterations: 110
optimal objective: 64759.2500
run time: 1.65e-03s
optimal rho estimate: 8.02e-03

[Peargrady]

My setting is:
OSQPSettings* settings = reinterpret_cast<OSQPSettings*>(c_malloc(sizeof(OSQPSettings)));
osqp_set_default_settings(settings);

settings->rho                   = 1.4e-2;
settings->adaptive_rho_interval = 25;
settings->eps_rel               = 5e-4;
settings->scaling               = 10;
settings->scaled_termination    = false;

settings->eps_abs           = 1e-4;
settings->eps_prim_inf      = 1e-4;
settings->eps_dual_inf      = 1e-4;
settings->polish            = true;
settings->check_termination = 10;
settings->verbose           = true;
settings->time_limit        = 0.05;

[Peargrady]

I'm confused about the second time, I have given a good initial guess for this problem. But why osqp still need 110 iterations to convergence? And in the second time, why objective is -3.5634e+06 in iter is 1? I think the objective should be 6.4706e+04.

[Peargrady]

I use the solved solution as warm start, my code is following: ============================my code======================================== // use result as warm start test std::vector<c_float> warm_start_x(num_of_knots_ * num_of_variables_per_moment_); std::vector<c_float> warm_start_y(num_of_knots_ * num_of_variables_per_moment_); for (int32_t i = 0; i < num_of_knots_ * num_of_variables_per_moment_; ++i) { warm_start_x[i] = work->solution->x[i]; warm_start_y[i] = work->solution->y[i]; } osqp_warm_start(work, CopyData(warm_start_x), CopyData(warm_start_y)); osqp_solve(work); ============================my code========================================

So sorrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrrry!!!!!!!!!!!!!!!!!!!!!!! It's my bug of construct warm_start_y, I misunderstood that warm_start_y's dimension is equal to warm_start_x. Actually, that's wrong... After correct it, my program works well.
Thanks osqp!