Thank you again for your help! Below is a sample output for a solved situation just to get an idea of the order of magnitude:

```
Calling Mosek 8.0.0.60: 28336 variables, 11637 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 : 11637
Cones : 6651
Scalar variables : 28336
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 : 3325
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.02
Lin. dep. - number : 0
Presolve terminated. Time: 0.03
Optimizer - threads : 4
Optimizer - solved problem : the primal
Optimizer - Constraints : 6649
Optimizer - Cones : 6651
Optimizer - Scalar variables : 25011 conic : 21684
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.05 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 1.55e+005 after factor : 3.57e+005
Factor - dense dim. : 75 flops : 3.19e+007
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.0e+000 3.9e+005 3.9e+005 0.00e+000 6.400210018e+009 -2.782299437e+003 1.0e+000 0.11
1 1.8e-001 7.2e+004 3.1e+004 -1.00e+000 6.396369143e+009 -3.930912055e+003 1.8e-001 0.17
2 6.0e-002 2.3e+004 5.7e+003 -9.98e-001 6.385384951e+009 -6.859354411e+003 6.0e-002 0.19
3 3.0e-002 1.2e+004 2.0e+003 -9.95e-001 6.366376179e+009 -1.119867508e+004 3.0e-002 0.22
4 1.3e-002 5.0e+003 5.8e+002 -9.88e-001 6.315284101e+009 -2.246086256e+004 1.3e-002 0.23
5 5.9e-003 2.3e+003 1.8e+002 -9.72e-001 6.213581898e+009 -4.499927636e+004 5.9e-003 0.27
6 1.2e-003 4.9e+002 1.9e+001 -9.41e-001 5.598613725e+009 -1.825256152e+005 1.2e-003 0.28
7 2.2e-004 8.4e+001 2.0e+000 -7.54e-001 3.520458318e+009 -6.502044719e+005 2.2e-004 0.31
8 3.4e-005 1.3e+001 3.7e-001 -1.02e-001 1.012272516e+009 -1.175907491e+006 3.4e-005 0.33
9 5.1e-006 2.0e+000 1.8e-001 7.70e-001 1.638053117e+008 -1.113784977e+006 5.1e-006 0.36
10 4.2e-007 1.6e-001 8.1e-002 1.27e+000 1.064602601e+007 -4.018514963e+005 4.2e-007 0.38
11 5.0e-008 2.0e-002 2.9e-002 1.15e+000 1.183400346e+006 -6.781713622e+004 5.0e-008 0.41
12 1.8e-009 7.1e-004 5.2e-003 1.02e+000 6.050470980e+003 -3.904609072e+004 1.8e-009 0.42
13 1.2e-009 4.6e-004 4.1e-003 9.95e-001 2.407058557e+003 -2.678061230e+004 1.2e-009 0.45
14 5.3e-010 2.1e-004 2.6e-003 1.00e+000 -1.283262097e+004 -2.577674210e+004 5.3e-010 0.47
15 1.3e-010 4.2e-005 1.1e-003 1.00e+000 -1.906667940e+004 -2.171202815e+004 1.1e-010 0.50
16 2.8e-011 1.1e-005 5.7e-004 1.02e+000 -1.949364083e+004 -2.015757276e+004 2.8e-011 0.52
17 1.7e-011 4.8e-006 3.8e-004 1.03e+000 -1.791555271e+004 -1.820435279e+004 1.2e-011 0.53
Interior-point optimizer terminated. Time: 0.55.
Optimizer terminated. Time: 0.56
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: -1.7915552707e+004 nrm: 3e+003 Viol. con: 1e-005 var: 5e-006 cones: 4e-006
Dual. obj: -1.8204352666e+004 nrm: 5e+006 Viol. con: 0e+000 var: 2e+000 cones: 0e+000
Optimizer summary
Optimizer - time: 0.56
Interior-point - iterations : 17 time: 0.55
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): +5819.47
cvx_slvtol =
1.2207e-04
```

However, I am running the above with

```
cvx_precision low
cvx_solver_settings('MSK_DPAR_INTPNT_CO_TOL_REL_GAP', 1e-2)
```

Are there any other tolerances that I could add on?

(I see the full list here https://docs.mosek.com/9.0/toolbox/param-groups.html#doc-param-groups)

Finally, if there might be a way for me to reduce the tolerances from [ϵ^3/8,ϵ^1/4,ϵ^1/4] then would be much appreciated. Thank you.