How to use Mosek command?

[li xing]

Dear Mosek Experts,

     Mosek version10.2

     Matlab version 2022a

     Computer system Windows 11 64bit

    I want to use commands to speed up calculation. 

 What commands can I use to control the following parameters:

1. ITE

2. PFEAS    
3. DFEAS    
4. GFEAS    
5. PRSTATUS  
6. POBJ              
7. DOBJ              
8. MU      
9. TIME

From link (https://docs.mosek.com/latest/cmdtools/solving-conic.html), I know that:

1. Command 'MSK_DPAR_INTPNT_CO_TOL_PFEAS' controls PFEAS

2. Command 'MSK_DPAR_INTPNT_CO_TOL_DFEAS' controls DFEAS

 Hope you can reply me. Thank you so much!

[Michal Adamaszek]

The major termination criteria are discussed in 

https://docs.mosek.com/latest/cmdtools/solving-conic.html#adjusting-optimality-criteria

All parameters can be found in

https://docs.mosek.com/latest/cmdtools/parameters.html#parameters-alphabetical-list-sorted-by-type

For an SDP solved by the interior point algorithm in 99.99% of the cases modifying the termination criteria is a bad idea since you will either stop too early and get a very bad solution or run into a stall. We do not recommend it.

From the log it all looks very reasonable and the solution is of good quality, but if you have doubts then please save a task file of the problem and contact Mosek support.

Michal

[li xing]

Thank you!

My research is about MIMO communication, so there are many antennas and the matrix dimension is very large, which makes Mosek a bit slow.

If I use the default Mosek settings, the code takes a long time to run. Therefore, I would like to adjust the Mosek settings appropriately to ensure the quality of the solution to a certain extent, while also reducing the code running time appropriately. However, I am not sure about the mutual influence between the following commands. Can you explain it?

Commands:

1. MSK_DPAR_INTPNT_CO_TOL_DFEAS，
2. MSK_DPAR_INTPNT_CO_TOL_INFEAS，
3. MSK_DPAR_INTPNT_CO_TOL_MU_RED，
4. MSK_DPAR_INTPNT_CO_TOL_NEAR_REL，
5. MSK_DPAR_INTPNT_CO_TOL_PFEAS，
6. MSK_DPAR_INTPNT_CO_TOL_REL_GAP
7. MSK_DPAR_INTPNT_TOL_DSAFE
8. MSK_DPAR_INTPNT_TOL_PSAFE

These  commands  can be viewed in the log, such as 'MSK_DPAR_INTPNT_CO_TOL_DFEAS----DFEAS' , 'MSK_DPAR_INTPNT_CO_TOL_MU_RED---MU',  'MSK_DPAR_INTPNT_CO_TOL_PFEAS----PFEAS', 'MSK_DPAR_INTPNT_CO_TOL_REL_GAP---GFEAS'.

However, other commands cannot be viewed in the log.

Therefore, when I set  commands  , I am not very clear about how these  commands  affect each other.

[li xing]

Is there a way to immediately stop optimizing when PRSTATUS=1?

'PRSTATUS=1' means that an optimal solution has been obtained as stated in the link (https://docs.mosek.com/latest/toolbox/solving-conic.html#interior-point-termination-criterion).

 

On Tuesday, October 29, 2024 at 3:57:59 PM UTC+8 Michal Adamaszek wrote:

[Erling D. Andersen]

A value of 1 means that the problem most like has optimal solution. It does NOT mean, that an optimal solution is known.

So your reading is simply wrong.

[Michal Adamaszek]

PRSTATUS is a heuristic indicator for general user orientation and no decisions are made based on that.

Not all parameters correspond one-to-one to entries in the log. The descriptions of parameters appear in https://docs.mosek.com/latest/toolbox/parameters.html#doc-dparam-list . It is impossible to say what would help in your case. Most of those parameters should not be touched.

Please remember that in the homogenous model if you stop the solve early then it will not only be far from optimal, but also far from feasible and far from dual feasible at a similar rate. Not sure if that is what you want. You can do it by modifying all the parameters from the table in https://docs.mosek.com/latest/toolbox/solving-conic.html#adjusting-optimality-criteria simultaneously at a similar rate.

Michal

[li xing]

Thank you! I have read the command guideline before (link  https://docs.mosek.com/latest/toolbox/parameters.html#doc-dparam-list   ), but I lack experience in using it, so I raised the question and consulted you.