Thanks Erling!
I tried by setting Mosek as the solver. It still reports Infeasible. Below is the log.
I don’t think my original problem is small, but probably ill posted. BTW, what is your definition of “ill posted” in this context. I checked the eigenvalues of H, they range from 7.4 to 4231. Do you think that would be an issue?
Calling Mosek 8.0.0.60: 20 variables, 10 equality constraints
For improved efficiency, Mosek is solving the dual problem.
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MOSEK Version 8.0.0.60 (Build date: 2017-3-1 13:08:15)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: MACOSX/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 10
Cones : 1
Scalar variables : 20
Matrix variables : 0
Integer variables : 0
Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator - tries : 0 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 10
Optimizer - Cones : 1
Optimizer - Scalar variables : 20 conic : 11
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 : 55 after factor : 55
Factor - dense dim. : 0 flops : 1.16e+03
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 4.3e+01 2.0e+00 1.0e+00 0.00e+00 0.000000000e+00 0.000000000e+00 1.0e+00 0.07
1 1.2e+01 5.8e-01 1.6e-01 -9.61e-01 -1.477103024e+04 -1.239807234e+04 2.8e-01 0.18
2 1.9e+00 9.0e-02 1.0e-02 -9.17e-01 -1.521790624e+05 -1.337839949e+05 4.5e-02 0.19
3 4.3e-01 2.0e-02 1.0e-03 -1.02e+00 -8.203214330e+05 -7.270882589e+05 9.9e-03 0.19
4 7.7e-02 3.6e-03 8.0e-05 -1.03e+00 -4.602185412e+06 -4.092154367e+06 1.8e-03 0.20
5 2.3e-02 1.1e-03 1.3e-05 -1.01e+00 -1.534627786e+07 -1.355901597e+07 5.3e-04 0.21
6 5.1e-03 2.4e-04 1.5e-06 -9.15e-01 -5.938465367e+07 -5.280980264e+07 1.2e-04 0.21
7 2.1e-03 9.8e-05 4.1e-07 -8.05e-01 -1.317777723e+08 -1.175475667e+08 4.8e-05 0.22
8 8.6e-04 4.0e-05 1.3e-07 -6.90e-01 -2.606955321e+08 -2.362378814e+08 2.0e-05 0.23
9 6.2e-04 2.9e-05 7.3e-08 -8.49e-01 -3.475929339e+08 -3.073592514e+08 1.4e-05 0.24
10 1.7e-04 7.9e-06 1.5e-08 -6.14e-01 -7.952656486e+08 -7.279292878e+08 3.9e-06 0.25
11 8.3e-05 3.9e-06 5.1e-09 -6.11e-01 -1.372043837e+09 -1.226971478e+09 1.9e-06 0.25
12 2.5e-05 1.2e-06 1.4e-09 -3.07e-01 -2.419664943e+09 -2.252133524e+09 5.7e-07 0.26
13 1.2e-05 5.4e-07 4.7e-10 -3.64e-01 -3.934811142e+09 -3.595866314e+09 2.7e-07 0.26
14 3.8e-06 1.8e-07 1.7e-10 4.44e-03 -5.517624836e+09 -5.238242709e+09 8.9e-08 0.27
15 1.9e-06 8.9e-08 5.5e-11 -3.25e-01 -8.518372321e+09 -7.882735003e+09 4.4e-08 0.28
16 5.3e-07 2.5e-08 2.0e-11 1.97e-01 -1.082937275e+10 -1.043513068e+10 1.2e-08 0.29
17 2.1e-07 1.0e-08 5.6e-12 -1.34e-01 -1.570796250e+10 -1.491996978e+10 4.9e-09 0.30
18 6.2e-08 2.9e-09 2.2e-12 3.91e-01 -1.798930307e+10 -1.755207597e+10 1.4e-09 0.30
19 2.6e-08 1.2e-09 7.3e-13 5.73e-02 -2.201673410e+10 -2.133380455e+10 6.0e-10 0.31
20 5.8e-09 2.7e-10 2.8e-13 6.47e-01 -2.313278214e+10 -2.289666973e+10 1.4e-10 0.32
21 1.7e-09 8.2e-11 1.0e-13 5.44e-01 -2.410348688e+10 -2.395063203e+10 4.0e-11 0.32
22 2.1e-10 9.8e-12 1.3e-14 9.05e-01 -2.423102718e+10 -2.421003436e+10 4.8e-12 0.33
23 1.6e-10 1.1e-12 1.7e-14 9.60e-01 -2.425153769e+10 -2.424900041e+10 5.4e-13 0.34
24 1.6e-10 1.1e-12 1.7e-14 9.90e-01 -2.425153769e+10 -2.424900041e+10 5.4e-13 0.34
Interior-point optimizer terminated. Time: 0.35.
MOSEK DUAL INFEASIBILITY REPORT.
Problem status: The problem is dual infeasible
Optimizer terminated. Time: 0.46
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : NEAR_DUAL_INFEASIBLE_CER
Primal. obj: -3.3135681203e+02 nrm: 3e+02 Viol. con: 2e-05 var: 0e+00 cones: 0e+00
Optimizer summary
Optimizer - time: 0.46
Interior-point - iterations : 25 time: 0.35
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
Mosek error: MSK_RES_TRM_STALL ()
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Status: Inaccurate/Infeasible
Optimal value (cvx_optval): +Inf