SDPT3: Infeasible path-following algorithms

[Hoai An Trinh]

Dear fellows,

I'm using solver SDPT3 in Matlab to solve the LMI with code:
A=[ -2.548 9.1 0;1 -1 0;0 -14.2 0];
B = [1 0 0;0 1 0;0 0 1];
P=1000000*eye(3);
F=sdpvar(3,3);
GH = (A' + F'*B')*P + P*(A + B*F);
const =(GH<0);
diagnostics= solvesdp(const);
F = double(F)

But the result is:
******SDPT3: Infeasible path-following algorithms******

Please help me to solve this problem.

[Johan Löfberg]

1. Strict inequalities are not supported. There should be a very sad cat telling you about this.

2. solvesdp is not an official command https://yalmip.github.io/tutorial/basics

3. and neither is double

4. the term 1000000 makes absolutely no sense. it just adds numerical garbage to the model, but since the model is homogeneous in P, the scaling can be removed without changing the feasible set

5. and what is the actual question? you don't show any result but simply parts of the header that sdpt3 displays. the problem solves nicely here

 num. of constraints =  6
 dim. of sdp    var  =  3,   num. of sdp  blk  =  1
*******************************************************************
   SDPT3: Infeasible path-following algorithms
*******************************************************************
 version  predcorr  gam  expon  scale_data
   HKM      1      0.000   1        0    
it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime
-------------------------------------------------------------------
 0|0.000|0.000|3.5e+07|1.9e+00|7.6e+08| 7.096000e+07  0.000000e+00| 0:0:00| chol  1  1
 1|0.989|1.000|3.8e+05|6.9e-09|8.3e+06| 7.734574e+05  0.000000e+00| 0:0:00| chol  1  1
 2|0.989|1.000|4.1e+03|6.9e-10|9.1e+04| 8.498974e+03  0.000000e+00| 0:0:00| chol  1  1
 3|0.989|1.000|4.6e+01|6.9e-11|1.0e+03| 9.339527e+01  0.000000e+00| 0:0:00| chol  1  1
 4|0.989|1.000|5.0e-01|6.9e-12|1.1e+01| 1.026322e+00  0.000000e+00| 0:0:00| chol  1  1
 5|0.989|1.000|5.5e-03|6.9e-13|1.2e-01| 1.127826e-02  0.000000e+00| 0:0:00| chol  1  1
 6|0.989|1.000|6.1e-05|6.9e-08|1.3e-03| 1.239369e-04  0.000000e+00| 0:0:00| chol  1  1
 7|0.989|1.000|6.6e-07|6.9e-08|1.5e-05| 1.361944e-06  0.000000e+00| 0:0:00| chol  1  1
 8|0.989|1.000|7.3e-09|6.9e-08|1.6e-07| 1.496642e-08  0.000000e+00| 0:0:00| chol  1  1
 9|0.989|1.000|8.0e-11|1.5e-09|1.8e-09| 1.644662e-10  0.000000e+00| 0:0:00|
  stop: max(relative gap, infeasibilities) < 1.00e-07
-------------------------------------------------------------------
 number of iterations   =  9
 primal objective value =  1.64466157e-10
 dual   objective value =  0.00000000e+00
 gap := trace(XZ)       = 1.77e-09
 relative gap           = 1.77e-09
 actual relative gap    = 1.64e-10
 rel. primal infeas     = 8.03e-11
 rel. dual   infeas     = 1.46e-09
 norm(X), norm(y), norm(Z) = 4.0e-17, 2.2e+01, 4.4e+07
 norm(A), norm(b), norm(C) = 6.0e+06, 1.0e+00, 2.5e+07
 Total CPU time (secs)  = 0.21  
 CPU time per iteration = 0.02  
 termination code       =  0
 DIMACS errors: 8.0e-11  0.0e+00  2.6e-09  0.0e+00  1.6e-10  1.8e-09
-------------------------------------------------------------------
diagnostics =
  struct with fields:


    yalmipversion: '20200116'
    matlabversion: '9.4.0.813654 (R2018a)'
       yalmiptime: 0.2420
       solvertime: 0.3210
             info: 'Successfully solved (SDPT3-4)'
          problem: 0

[Hoai An Trinh]

Dear Sir, 

Thanks for your answer.

Because I simulate an example from the book as follows

But my simulation result is not the same as above

I wonder whether there are some mistakes in my code or installing Yalmip toolbox causing the different results. 

I also simulate other examples and the results are different.  

Can you help me with solutions to solve this problem?

Thanks.

Vào lúc 18:43:35 UTC+9 ngày Thứ Tư, 1 tháng 7, 2020, Johan Löfberg đã viết:

[Johan Löfberg]

you are solving a feasibility problem so the solution is not unique

[Muhammad Yasir]

What do ' DIMACS errors stand for? I am also getting this message in my simulatios:

"

num. of constraints = 54

 dim. of socp   var  = 27,   num. of socp blk  =  1

 dim. of linear var  = 59

*******************************************************************

   SDPT3: Infeasible path-following algorithms

*******************************************************************

 version  predcorr  gam  expon  scale_data

   HKM      1      0.000   1        0    

it pstep dstep pinfeas dinfeas  gap      prim-obj      dual-obj    cputime

-------------------------------------------------------------------

 0|0.000|0.000|1.5e+01|1.8e+00|1.3e+07|-5.819363e+06  0.000000e+00| 0:0:00| chol  1  1 

 1|0.943|0.687|8.6e-01|5.8e-01|4.2e+06| 6.009947e+04 -2.044550e+04| 0:0:00| chol  1  1 

 2|1.000|0.907|1.2e-07|5.4e-02|5.9e+05| 2.294166e+05 -2.839086e+04| 0:0:00| chol  1  1 

 3|1.000|0.960|1.2e-07|2.2e-03|6.4e+04| 2.775807e+04 -2.221093e+04| 0:0:00| chol  1  1 

 4|0.625|0.902|1.3e-07|2.2e-04|3.3e+04| 8.862582e+03 -2.070572e+04| 0:0:00| chol  1  1 

 5|0.581|0.544|6.4e-08|1.0e-04|2.1e+04| 4.236636e+02 -1.893067e+04| 0:0:00| chol  1  1 

 6|0.623|1.000|2.5e-08|6.3e-06|1.4e+04|-5.812588e+03 -1.965088e+04| 0:0:00| chol  1  1 

 7|1.000|1.000|1.4e-09|1.9e-06|6.0e+03|-1.283317e+04 -1.873347e+04| 0:0:00| chol  1  1 

 8|0.706|0.814|8.4e-10|8.1e-07|3.4e+03|-1.462840e+04 -1.796916e+04| 0:0:00| chol  1  1 

 9|1.000|1.000|3.5e-10|1.7e-07|1.6e+03|-1.615892e+04 -1.773258e+04| 0:0:00| chol  1  1 

10|1.000|1.000|5.1e-13|5.1e-08|4.0e+02|-1.699829e+04 -1.740118e+04| 0:0:00| chol  1  1 

11|0.947|1.000|4.9e-14|1.5e-08|1.4e+02|-1.714943e+04 -1.728566e+04| 0:0:00| chol  1  1 

12|1.000|1.000|2.7e-12|4.6e-09|4.3e+01|-1.720077e+04 -1.724379e+04| 0:0:00| chol  1  1 

13|0.949|1.000|9.9e-13|1.4e-09|9.5e+00|-1.721643e+04 -1.722591e+04| 0:0:00| chol  1  1 

14|1.000|0.930|1.4e-12|4.8e-10|1.2e+00|-1.721968e+04 -1.722083e+04| 0:0:00| chol  1  1 

15|0.986|0.950|1.2e-11|2.5e-11|1.1e-01|-1.721992e+04 -1.722002e+04| 0:0:00| chol  1  1 

16|0.980|0.964|2.4e-12|2.4e-12|4.0e-03|-1.721994e+04 -1.721994e+04| 0:0:00| chol  1  1 

17|0.983|0.982|1.2e-12|5.4e-13|7.8e-05|-1.721994e+04 -1.721994e+04| 0:0:00|

  stop: max(relative gap, infeasibilities) < 1.00e-07

-------------------------------------------------------------------

 number of iterations   = 17

 primal objective value = -1.72199374e+04

 dual   objective value = -1.72199374e+04

 gap := trace(XZ)       = 7.83e-05

 relative gap           = 2.27e-09

 actual relative gap    = 2.05e-09

 rel. primal infeas     = 1.18e-12

 rel. dual   infeas     = 5.37e-13

 norm(X), norm(y), norm(Z) = 3.5e+03, 1.7e+04, 4.9e+03

 norm(A), norm(b), norm(C) = 4.6e+01, 1.7e+03, 1.9e+04

 Total CPU time (secs)  = 0.06  

 CPU time per iteration = 0.00  

 termination code       =  0

 DIMACS errors: 1.2e-12  0.0e+00  7.6e-13  0.0e+00  2.0e-09  2.3e-09

-------------------------------------------------------------------

[Johan Löfberg]

http://plato.asu.edu/dimacs/

[Muhammad Yasir]

Sir, I have gone through the link that you have shared. I could not understand it. Could you please explain in simple words, what do 'DIMACS errors' stand for?

Is it indicating some erratic behaviour in my simulations?

[Johan Löfberg]

dimacs error measures are just somewhat standardized measures of optimality and feasibility used (some 25 years ago...) to compare different solvers