I am trying to solve a LP on a rolling basis and run into infeasible solns. on some instances.

I have the following settings in my optimizer:

```
cvx_precision low
cvx_solver_settings('MSK_DPAR_INTPNT_CO_TOL_REL_GAP', 1e-5)
```

and am wondering if there are other tolerances that I can add/control for my case below? I don’t case about the accuracy from the 100’s term and lower.

Here is the output of a feasible problem:

```
Calling Mosek 8.0.0.60: 60773 variables, 23605 equality constraints
For improved efficiency, Mosek is solving the dual problem.
------------------------------------------------------------
NOTE: custom settings have been set for this solver.
------------------------------------------------------------
MOSEK Version 8.0.0.60 (Build date: 2017-3-1 13:09:33)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 23605
Cones : 18547
Scalar variables : 60773
Matrix variables : 0
Integer variables : 0
Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 3373
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.00
Lin. dep. - number : 0
Presolve terminated. Time: 0.05
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 20231
Optimizer - Cones : 18547
Optimizer - Scalar variables : 57400 conic : 54026
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.14 dense det. time : 0.00
Factor - ML order time : 0.02 GP order time : 0.00
Factor - nonzeros before factor : 1.97e+005 after factor : 6.01e+005
Factor - dense dim. : 71 flops : 4.68e+007
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.5e+000 3.9e+005 3.9e+005 0.00e+000 6.416504224e+009 1.564099246e+007 1.0e+000 0.22
1 4.1e-001 1.1e+005 5.6e+004 -1.00e+000 6.414217523e+009 1.562857217e+007 2.7e-001 0.30
2 1.0e-001 2.7e+004 7.1e+003 -9.99e-001 6.404582721e+009 1.556580049e+007 6.9e-002 0.34
3 3.3e-002 8.7e+003 1.3e+003 -9.96e-001 6.375242412e+009 1.536613260e+007 2.2e-002 0.39
4 9.1e-003 2.4e+003 1.9e+002 -9.86e-001 6.257904133e+009 1.458447363e+007 6.1e-003 0.44
5 2.4e-003 6.2e+002 2.7e+001 -9.50e-001 5.838827811e+009 1.189262268e+007 1.6e-003 0.48
6 5.7e-004 1.5e+002 3.8e+000 -8.23e-001 4.521543310e+009 3.722387101e+006 3.8e-004 0.53
7 1.4e-004 3.7e+001 8.7e-001 -4.14e-001 2.377836021e+009 -9.030469796e+006 9.6e-005 0.56
8 2.9e-005 7.7e+000 3.3e-001 3.03e-001 6.312464149e+008 -1.768561643e+007 2.0e-005 0.61
9 8.7e-006 2.3e+000 2.9e-001 1.28e+000 1.275436212e+008 -1.369178577e+007 5.8e-006 0.66
10 1.6e-006 4.2e-001 1.5e-001 2.14e+000 6.757146502e+006 -7.550900666e+006 1.1e-006 0.70
11 2.4e-007 6.2e-002 6.1e-002 1.12e+000 -4.103955629e+006 -6.080254238e+006 1.6e-007 0.75
12 4.4e-008 1.1e-002 3.1e-002 1.08e+000 -3.631419460e+006 -3.973389390e+006 2.9e-008 0.80
13 1.0e-008 2.7e-003 1.9e-002 1.19e+000 -1.459945630e+006 -1.531507141e+006 6.9e-009 0.83
14 8.2e-009 2.1e-003 1.7e-002 1.11e+000 -1.026719937e+006 -1.083326261e+006 5.4e-009 0.88
15 4.8e-009 1.3e-003 1.3e-002 1.04e+000 -3.830980021e+005 -4.172662801e+005 3.2e-009 0.92
16 3.6e-009 9.4e-004 1.1e-002 9.18e-001 -1.402827167e+005 -1.666501804e+005 2.4e-009 0.97
17 2.9e-009 7.5e-004 9.3e-003 8.33e-001 9.973788067e+003 -1.200208703e+004 1.9e-009 1.01
18 2.6e-009 6.7e-004 8.7e-003 7.72e-001 7.967928588e+004 5.949420147e+004 1.7e-009 1.06
19 2.5e-009 6.4e-004 8.4e-003 7.49e-001 1.096491331e+005 9.021655514e+004 1.6e-009 1.11
20 1.8e-009 4.7e-004 6.8e-003 7.34e-001 2.828544366e+005 2.675783314e+005 1.2e-009 1.14
21 1.5e-009 4.0e-004 6.1e-003 7.06e-001 3.575170844e+005 3.440682334e+005 1.0e-009 1.19
22 8.8e-010 2.3e-004 4.2e-003 6.72e-001 5.861238271e+005 5.773417968e+005 5.9e-010 1.23
23 5.6e-010 1.5e-004 3.0e-003 5.72e-001 7.556985751e+005 7.492953782e+005 3.7e-010 1.28
24 4.4e-010 1.1e-004 2.5e-003 5.28e-001 8.353204662e+005 8.298869190e+005 2.9e-010 1.33
25 2.8e-010 7.2e-005 1.7e-003 4.81e-001 9.742746298e+005 9.702427669e+005 1.8e-010 1.38
26 1.9e-010 4.6e-005 1.2e-003 4.51e-001 1.094781349e+006 1.091766272e+006 1.2e-010 1.42
27 1.6e-010 4.1e-005 1.1e-003 4.50e-001 1.123557540e+006 1.120765025e+006 1.0e-010 1.47
28 1.5e-010 3.8e-005 1.1e-003 4.86e-001 1.134054479e+006 1.131455395e+006 9.8e-011 1.50
29 1.4e-010 2.0e-005 6.6e-004 4.62e-001 1.262552716e+006 1.260866661e+006 5.2e-011 1.56
30 6.9e-011 1.0e-005 3.8e-004 5.04e-001 1.380267434e+006 1.379275127e+006 2.6e-011 1.59
31 5.2e-011 7.6e-006 3.1e-004 5.91e-001 1.414480471e+006 1.413681112e+006 1.9e-011 1.72
32 2.9e-011 4.2e-006 2.1e-004 6.60e-001 1.470582700e+006 1.470090577e+006 1.1e-011 1.84
33 1.3e-011 1.8e-006 1.2e-004 7.37e-001 1.519239938e+006 1.519004588e+006 4.7e-012 1.97
34 1.1e-010 6.4e-007 7.0e-005 9.50e-001 1.549923146e+006 1.549840016e+006 1.7e-012 2.08
Interior-point optimizer terminated. Time: 2.08.
Optimizer terminated. Time: 2.11
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 1.5499231460e+006 nrm: 9e+004 Viol. con: 5e-004 var: 1e-006 cones: 0e+000
Dual. obj: 1.5498398096e+006 nrm: 3e+009 Viol. con: 0e+000 var: 7e-001 cones: 0e+000
Optimizer summary
Optimizer - time: 2.11
Interior-point - iterations : 34 time: 2.08
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): -1.79088e+07
cvx_slvtol =
1.2207e-04
```

Below is the output of the infeasible soln. at another instance:

```
Calling Mosek 8.0.0.60: 60773 variables, 23605 equality constraints
For improved efficiency, Mosek is solving the dual problem.
------------------------------------------------------------
NOTE: custom settings have been set for this solver.
------------------------------------------------------------
MOSEK Version 8.0.0.60 (Build date: 2017-3-1 13:09:33)
Copyright (c) MOSEK ApS, Denmark. WWW: mosek.com
Platform: Windows/64-X86
Problem
Name :
Objective sense : min
Type : CONIC (conic optimization problem)
Constraints : 23605
Cones : 18547
Scalar variables : 60773
Matrix variables : 0
Integer variables : 0
Optimizer started.
Conic interior-point optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 3373
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.02
Lin. dep. - number : 0
Presolve terminated. Time: 0.05
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 20231
Optimizer - Cones : 18547
Optimizer - Scalar variables : 57400 conic : 54026
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.11 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 1.97e+005 after factor : 6.01e+005
Factor - dense dim. : 71 flops : 4.68e+007
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.5e+000 3.9e+005 3.9e+005 0.00e+000 6.451078621e+009 5.021538870e+007 1.0e+000 0.20
1 4.1e-001 1.1e+005 5.6e+004 -1.00e+000 6.448780107e+009 5.019079931e+007 2.7e-001 0.27
2 1.0e-001 2.6e+004 6.9e+003 -9.99e-001 6.438809384e+009 5.007394463e+007 6.7e-002 0.31
3 3.4e-002 8.9e+003 1.3e+003 -9.96e-001 6.410449293e+009 4.973308855e+007 2.3e-002 0.36
4 9.3e-003 2.4e+003 2.0e+002 -9.87e-001 6.295363157e+009 4.836393549e+007 6.2e-003 0.41
5 2.5e-003 6.4e+002 2.8e+001 -9.52e-001 5.887955815e+009 4.361539188e+007 1.6e-003 0.45
6 7.0e-004 1.8e+002 5.0e+000 -8.28e-001 4.812323204e+009 3.129855102e+007 4.6e-004 0.50
7 1.8e-004 4.7e+001 1.1e+000 -4.97e-001 2.767876314e+009 8.184102411e+006 1.2e-004 0.55
8 3.7e-005 9.6e+000 3.6e-001 1.70e-001 7.916571161e+008 -1.285301426e+007 2.4e-005 0.59
9 1.0e-005 2.6e+000 2.9e-001 1.12e+000 1.647061739e+008 -1.373332629e+007 6.8e-006 0.63
10 2.3e-006 5.9e-001 2.0e-001 2.14e+000 1.329574279e+007 -7.877815395e+006 1.5e-006 0.67
11 2.8e-007 7.4e-002 7.7e-002 1.22e+000 -4.015970031e+006 -6.384864728e+006 1.9e-007 0.72
Interior-point optimizer terminated. Time: 0.73.
MOSEK DUAL INFEASIBILITY REPORT.
Problem status: The problem is dual infeasible
Optimizer terminated. Time: 0.77
Interior-point solution summary
Problem status : DUAL_INFEASIBLE
Solution status : DUAL_INFEASIBLE_CER
Primal. obj: -2.7510744688e+004 nrm: 7e+000 Viol. con: 4e-004 var: 3e-004 cones: 2e-004
Optimizer summary
Optimizer - time: 0.77
Interior-point - iterations : 11 time: 0.73
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: Infeasible
Optimal value (cvx_optval): +Inf
cvx_slvtol =
1.2207e-04
```