Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN

[Iser (ABABACAR GAYE)]

I get this alert message only when I vary the total bandwidth B. For example when I use a 5 MHz band, the warning disappear but I need to test with other values. thank you for helping me.

Here is my code.

clc
clear all
rng(‘default’) % For reproducibility
I = 50;
eps1 = 10^-2;
eps2 = 10^-2;
fmax = 20 * 10^9;
s = normrnd(1000, 100, I, 1) * 8000 ;
c = normrnd(1000, 100, I, 1) * 10^6 ;
fl = c;
B = 10 * 10^6;
rfix = [0.5, 1, 1.5, 2, 2.5, 2.5, 2, 1.5, 1, 0.5];
cvx_begin
variable a(I) nonnegative
variable beta(I) nonnegative
variable fs(I) nonnegative
variable b(I) nonnegative
variable mu(I) nonnegative
variable omega(I) nonnegative
variable gamma(I) nonnegative

maximize sum(a)
subject to
0 <= a <= 1;

1./ (a * fmax + eps2) <= gamma <= 1/ eps1;
sum(inv_pos(gamma)) <= (fmax + I * eps2);
inv_pos(a .* B + eps1) <= beta <= 1/ eps1;
sum(inv_pos(beta)) <= B + I * eps1;
mu - a./ (B +eps1) >= 0;
beta - 1/(B + eps1) - mu + a/(B + eps1) >=  0;
a/eps1 - mu >= 0;
1/eps1 - beta - a/eps1 + mu >= 0;
omega - a/(fmax + eps2) >= 0;
gamma - 1/(fmax + eps2) - omega + a/(fmax +eps2) >=0;
a/eps2 - omega >= 0;
1/eps2 - gamma - a/eps2 + omega >=0;

(s .* mu / rfix(1) + c .* omega) + (1 - a) .* c ./ fl <= 4;

cvx_end

The results of the execution and the warnings

Calling SDPT3 4.0: 1502 variables, 450 equality constraints
For improved efficiency, SDPT3 is solving the dual problem.

num. of constraints = 450
dim. of socp var = 600, num. of socp blk = 200
dim. of linear var = 902
number of nearly dependent constraints = 400
To remove these constraints, re-run sqlp.m with OPTIONS.rmdepconstr = 1.

---

SDPT3: Infeasible path-following algorithms

---

version predcorr gam expon scale_data
NT 1 0.000 1 0
it pstep dstep pinfeas dinfeas gap prim-obj dual-obj cputime

0|0.000|0.000|2.1e+11|1.4e+01|4.1e+13| 2.450775e+10 0.000000e+00| 0:0:00| chol 2 3
1|0.968|0.890|6.8e+09|1.6e+00|4.2e+12| 2.442247e+10 3.302277e+01| 0:0:00| chol 3 3
2|0.947|0.924|3.6e+08|1.2e-01|3.7e+11| 1.802260e+10 5.021911e+01| 0:0:00| chol 2 2
3|0.700|0.953|1.1e+08|5.6e-03|2.5e+10| 6.103069e+09 1.024624e+02| 0:0:01| chol 2 2
4|0.960|0.958|4.4e+06|2.3e-04|1.0e+09| 2.690918e+08 1.284588e+02| 0:0:01| chol 2 2
5|0.984|0.982|7.0e+04|4.2e-06|2.2e+07| 8.711726e+06 1.302271e+02| 0:0:01| chol 1 1
6|0.973|0.934|1.9e+03|2.8e-07|1.6e+06| 8.461857e+05 6.013296e+01| 0:0:01| chol 1 1
7|0.984|0.889|3.1e+01|3.0e-08|1.8e+05| 1.298459e+05 4.316344e+01| 0:0:01| chol 1 1
8|0.846|0.588|4.7e+00|1.3e-08|5.1e+04| 3.143642e+04 3.967161e+01| 0:0:01| chol 1 1
9|0.815|0.723|8.8e-01|3.5e-09|2.3e+04| 1.642223e+04 2.828335e+01| 0:0:01| chol 1 1
10|0.983|0.938|1.5e-02|2.2e-10|1.2e+03| 9.357944e+02 2.741408e+01| 0:0:01| chol 1 1
11|0.961|0.986|5.9e-04|3.3e-12|4.5e+01| 6.535298e+01 2.887973e+01| 0:0:01| chol 1 1
12|1.000|0.910|7.5e-09|3.4e-13|6.5e+00| 5.271521e+01 4.770450e+01| 0:0:01| chol 1 1
13|0.932|0.980|5.9e-09|8.9e-15|2.9e-01| 5.018289e+01 4.995254e+01| 0:0:01| chol 1 1
14|0.985|0.988|9.6e-10|9.1e-16|5.5e-03| 5.000224e+01 4.999943e+01| 0:0:01| chol 1 1
15|0.981|0.944|7.8e-10|1.1e-15|2.7e-04| 5.000000e+01 4.999997e+01| 0:0:01| chol 1 1
16|0.979|1.000|2.7e-10|7.8e-16|7.2e-05| 5.000004e+01 4.999998e+01| 0:0:01| chol 1 1
17|0.774|1.000|7.4e-10|7.6e-16|2.5e-05| 5.000001e+01 4.999999e+01| 0:0:02| chol
linsysolve: Schur complement matrix not positive definite
switch to LU factor. lu Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 47)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

Warning: Matrix is singular, close to singular or badly scaled. Results may be inaccurate. RCOND = NaN.

In linsysolvefun (line 29)
In symqmr>precond (line 122)
In symqmr (line 69)
In linsysolve (line 220)
In NTpred (line 60)
In sqlpmain (line 345)
In sdpt3 (line 267)
In cvx_run_solver (line 56)
In cvx_sdpt3>solve (line 288)
In cvx_solve (line 399)
In cvx_finish (line 57)
In cvx_end (line 11)
In p5 (line 47)

30
stop: steps in predictor too short: pstep = 0.00e+00, dstep = 1.00e+00

18|0.000|1.000|7.4e-10|7.6e-16|2.5e-05| 5.000001e+01 4.999999e+01| 0:0:02|

number of iterations = 18
primal objective value = 5.00000109e+01
dual objective value = 4.99999940e+01
gap := trace(XZ) = 2.47e-05
relative gap = 2.45e-07
actual relative gap = 1.67e-07
rel. primal infeas (scaled problem) = 7.44e-10
rel. dual " " " = 7.57e-16
rel. primal infeas (unscaled problem) = 0.00e+00
rel. dual " " " = 0.00e+00
norm(X), norm(y), norm(Z) = 3.5e+02, 1.4e+11, 1.4e+11
norm(A), norm(b), norm© = 7.1e+09, 1.0e+00, 2.0e+10
Total CPU time (secs) = 1.92
CPU time per iteration = 0.11
termination code = -2
DIMACS: 7.4e-10 0.0e+00 1.1e-15 0.0e+00 1.7e-07 2.4e-07

---

Status: Inaccurate/Solved
Optimal value (cvx_optval): +50

[Mark_L_Stone]

You apparently didn’t take my advice to heart from your previous question Invalid quadratic : not a square ti improve the scaling of the input data. SDPT3 is not robust enough to handle your problem, and encountered severe numerical difficulties.

Mosek is much more robust, and claimed to solve the problem I ran (see below), with optimal objective value = 6.1905, despite issuing warnings for large input numbers.

CVX made me change the names of beta and gamma due to name conflict, so I added 1 to the end of those variable names. I also had to use inv_pos on the LHS of the 2nd constraint. How was your code ever accepted by CVX?

SeDuMi provided a different answer.

Bottom line: Don’t use very large or small magnitude numbers in your input data. Until that is fixed, I don’t trust any of these results.

 rng('default') % For reproducibility
    I = 50;
    eps1 = 10^-2;
    eps2 = 10^-2;
    fmax = 20 * 10^9;
    s = normrnd(1000, 100, I, 1) * 8000 ;
    c = normrnd(1000, 100, I, 1) * 10^6 ;
    fl = c;
    B = 10 * 10^6;
    rfix = [0.5, 1, 1.5, 2, 2.5, 2.5, 2, 1.5, 1, 0.5];
    cvx_begin
    variable a(I) nonnegative
    variable beta1(I) nonnegative
    variable fs(I) nonnegative
    variable b(I) nonnegative
    variable mu(I) nonnegative
    variable omega(I) nonnegative
    variable gamma1(I) nonnegative

maximize sum(a)
subject to
0 <= a <= 1;

inv_pos(a * fmax + eps2) <= gamma1 <= 1/ eps1; % Reformulated so that it would be accepted by CVX
sum(inv_pos(gamma1)) <= (fmax + I * eps2);
inv_pos(a .* B + eps1) <= beta1 <= 1/ eps1;
sum(inv_pos(beta1)) <= B + I * eps1;
mu - a./ (B +eps1) >= 0;
beta1 - 1/(B + eps1) - mu + a/(B + eps1) >=  0;
a/eps1 - mu >= 0;
1/eps1 - beta1 - a/eps1 + mu >= 0;
omega - a/(fmax + eps2) >= 0;
gamma1 - 1/(fmax + eps2) - omega + a/(fmax +eps2) >=0;
a/eps2 - omega >= 0;
1/eps2 - gamma1 - a/eps2 + omega >=0;

(s .* mu / rfix(1) + c .* omega) + (1 - a) .* c ./ fl <= 4;

    cvx_end

MOSEK Version 9.3.10 (Build date: 2021-11-5 08:42:07)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86

MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (98) at variable ‘’ (1002).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (99) at variable ‘’ (1005).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (100) at variable ‘’ (1008).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (101) at variable ‘’ (1011).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (102) at variable ‘’ (1014).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (103) at variable ‘’ (1017).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (104) at variable ‘’ (1020).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (105) at variable ‘’ (1023).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (106) at variable ‘’ (1026).
MOSEK warning 62: The A matrix contains a large value of 2.8e+10 in constraint ‘’ (107) at variable ‘’ (1029).
Warning number 62 is disabled.
MOSEK warning 57: A large value of 2.8e+10 has been specified in c for variable ‘’ (1154).
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 450
Cones : 200
Scalar variables : 1602
Matrix variables : 0
Integer variables : 0

Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 102
Eliminator terminated.
Eliminator started.
Freed constraints in eliminator : 50
Eliminator terminated.
Eliminator - tries : 2 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.08
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 450
Cones : 200
Scalar variables : 1602
Matrix variables : 0
Integer variables : 0

Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 298
Optimizer - Cones : 200
Optimizer - Scalar variables : 1250 conic : 600
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.00 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 3096 after factor : 4770
Factor - dense dim. : 0 flops : 2.30e+05
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+00 3.4e+10 2.0e+10 0.00e+00 2.001002000e+10 0.000000000e+00 1.0e+00 0.09
1 1.1e-01 3.9e+09 6.3e+09 -1.00e+00 1.873998922e+10 1.208292594e-08 1.1e-01 0.23
2 2.6e-02 8.9e+08 3.0e+09 -1.00e+00 1.877367541e+10 8.644864668e-08 2.6e-02 0.23
3 3.0e-03 1.0e+08 1.0e+09 -1.00e+00 1.875236684e+10 8.177545440e-07 3.0e-03 0.23
4 2.2e-04 7.6e+06 2.8e+08 -1.00e+00 1.874846805e+10 1.207606514e-05 2.2e-04 0.25
5 8.8e-06 3.0e+05 5.5e+07 -1.00e+00 1.874741792e+10 3.397746678e-04 8.7e-06 0.25
6 2.4e-07 4.8e+03 7.0e+06 -1.00e+00 1.872665095e+10 2.243146617e-02 1.4e-07 0.25
7 8.7e-08 1.2e+03 3.5e+06 -9.98e-01 1.864933013e+10 8.516546811e-02 3.5e-08 0.27
8 4.9e-08 3.9e+02 1.9e+06 -9.85e-01 1.807153993e+10 2.357801337e-01 1.1e-08 0.27
9 3.6e-09 2.4e+01 3.7e+05 -9.28e-01 1.077487966e+10 2.454925923e+00 7.0e-10 0.28
10 3.3e-10 1.8e+00 2.5e+04 -1.52e-01 1.209778163e+09 5.398326420e+00 5.3e-11 0.28
11 1.5e-12 5.5e-03 6.3e+00 8.64e-01 1.454646902e+06 5.851989772e+00 1.6e-13 0.28
12 5.7e-15 2.1e-05 1.5e-03 1.00e+00 5.689460865e+03 5.853456439e+00 6.2e-16 0.30
13 2.2e-17 8.4e-08 3.8e-07 1.00e+00 2.801616259e+01 5.853493334e+00 2.4e-18 0.30
14 4.3e-20 4.5e-08 3.6e-11 9.99e-01 5.870572687e+00 5.859033543e+00 5.8e-21 0.30
15 6.0e-20 4.1e-08 6.9e-12 8.15e-01 6.182111863e+00 6.167744039e+00 1.9e-21 0.31
16 7.5e-20 4.6e-08 3.0e-16 9.91e-01 6.189899110e+00 6.189599844e+00 7.6e-24 0.31
17 7.5e-20 2.8e-08 2.1e-22 1.00e+00 6.190498339e+00 6.190498339e+00 9.9e-28 0.33
Optimizer terminated. Time: 0.39

Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 6.1904983387e+00 nrm: 4e+00 Viol. con: 1e+00 var: 4e-10 cones: 7e-23
Dual. obj: 6.1904983390e+00 nrm: 4e+09 Viol. con: 0e+00 var: 6e+01 cones: 0e+00
Optimizer summary
Optimizer - time: 0.39
Interior-point - iterations : 17 time: 0.33
Basis identification - time: 0.00
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.00
Clean primal - iterations : 0 time: 0.00
Clean dual - iterations : 0 time: 0.00
Simplex - time: 0.00
Primal simplex - iterations : 0 time: 0.00
Dual simplex - iterations : 0 time: 0.00
Mixed integer - relaxations: 0 time: 0.00

---

Status: Solved
Optimal value (cvx_optval): +6.1905

+++++++++++++++++++++++++++++++
Running it in SeDuMi provided optimal objective value of 50.0054.
Calling SeDuMi 1.3.4: 1602 variables, 450 equality constraints
For improved efficiency, SeDuMi is solving the dual problem.

SeDuMi 1.3.4 by AdvOL, 2005-2008 and Jos F. Sturm, 1998-2003.
Alg = 2: xz-corrector, Adaptive Step-Differentiation, theta = 0.250, beta = 0.500
eqs m = 450, order n = 1403, dim = 1603, blocks = 201
nnz(A) = 2694 + 204, nnz(ADA) = 1746, nnz(L) = 1098
Handling 4 + 2 dense columns.
it : by gap delta rate t/tP t/tD* feas cg cg prec
0 : 4.18E+08 0.000
1 : 2.06E+01 1.78E+08 0.000 0.4259 0.9000 0.9000 1.30 92 1 2.4E+10
2 : 3.22E+01 1.49E+07 0.000 0.0834 0.9281 0.9000 0.84 55 39 2.0E+09
3 : 2.35E+01 4.30E+06 0.000 0.2895 0.0000 0.9000 2.83 16 23 2.0E+09
4 : 2.35E+01 6.26E+05 0.305 0.1456 0.9000 0.0000 4.83 8 15 4.8E+08
5 : 1.66E+01 4.16E+05 0.000 0.6634 0.9000 0.9000 2.00 16 16 1.6E+08
6 : 1.66E+01 1.99E+04 0.375 0.0479 0.9000 0.0000 2.47 15 15 2.3E+07
7 : 1.66E+01 1.01E+04 0.081 0.5082 0.9000 0.9000 1.82 15 15 6.2E+06
8 : 1.98E+01 6.93E+03 0.000 0.6848 0.4500 0.4500 1.71 15 15 3.5E+06
9 : 2.81E+01 3.28E+03 0.046 0.4734 0.9000 0.9000 1.69 8 8 1.0E+06
10 : 1.61E+01 2.68E+03 0.098 0.8157 0.9000 0.9000 4.93 10 10 3.1E+05
11 : 1.58E+01 1.11E+02 0.366 0.0414 0.9000 0.0000 9.99 11 11 1.6E+04
12 : 7.73E+00 7.77E+01 0.000 0.7008 0.9000 0.9000 5.01 8 8 3.5E+03
13 : 7.73E+00 2.47E+00 0.045 0.0318 0.9000 0.0000 6.47 10 10 2.2E+02
14 : 7.36E+00 5.56E-01 0.000 0.2253 0.9000 0.9000 1.38 7 8 3.8E+01
15 : 6.17E+00 5.15E-02 0.000 0.0927 0.9900 0.9900 1.67 3 3 2.4E+00
16 : 1.59E+01 3.20E-03 0.023 0.0622 0.9000 0.4384 -0.11 2 2 2.4E+00
17 : 7.57E+01 6.75E-04 0.000 0.2108 0.9000 0.9000 -0.99 1 2 2.4E+00
18 : 2.46E+03 1.73E-05 0.000 0.0256 0.9900 0.9900 -0.99 1 1 2.0E+00
19 : 7.68E+02 4.19E-06 0.000 0.2427 0.9005 0.9000 0.61 1 1 4.6E-01
20 : 1.87E+02 4.82E-08 0.000 0.0115 0.9285 0.9000 3.44 1 1 7.1E-03
21 : 7.77E+01 2.69E-09 0.000 0.0559 0.9210 0.9000 2.96 1 1 3.9E-04
22 : 7.77E+01 1.50E-10 0.000 0.0559 0.9000 0.0000 1.69 1 1 6.5E-05
23 : 5.80E+01 4.76E-11 0.000 0.3162 0.9000 0.9000 1.20 1 1 1.9E-05
24 : 5.80E+01 5.46E-12 0.148 0.1148 0.9000 0.0000 1.12 1 1 6.0E-06
25 : 5.19E+01 1.70E-13 0.000 0.0311 0.9146 0.9000 1.07 1 1 4.8E-07
26 : 5.01E+01 1.10E-14 0.000 0.0645 0.9900 0.9900 1.14 1 9 2.7E-08
27 : 5.00E+01 9.06E-16 0.000 0.0826 0.9900 0.9900 1.17 7 7 1.6E-09

iter seconds digits cx by
27 1.6 Inf 5.0000835079e+01 5.0005424578e+01
|Ax-b| = 1.0e-04, [Ay-c]_+ = 6.6E-03, |x|= 6.9e-02, |y|= 1.7e+09

Detailed timing (sec)
Pre IPM Post
2.230E-01 1.172E+00 2.500E-02
Max-norms: ||b||=1, ||c|| = 2.000000e+10,
Cholesky |add|=49, |skip| = 50, ||L.L|| = 98.0484.

Status: Solved
Optimal value (cvx_optval): +50.0054