Hi there,
Firstly, thanks for this useful toolbox.
My problem is:
I am running a CVX code with Mosek as the solver. I need to solve an LP for a high number of constraints let’s say 10^5 to 10^8. When I run the code in MATLAB, and check the activity monitor in my iMac, MATLAB only utilizes 10% of RAM. It works but takes lots of time. Is there a way to use the full capacity of RAM to make CVX faster?
Is there any setting in CVX to make it able to use a higher amount of RAM?
I should add that my code is not parallelizable. Besides, as far as I know, MATLAB uses as much RAM as it needs.
All the best,
The general answer is no. You may want to post the Mosek log output to check if that looks reasonable.
Thanks for your answer, where can I find teh Mosek log output?
Provided you don’t use the quiet option for CVX, the solver output will appear in your MATLAB console after cvx_end and some CVX pleasantries (such as informing you that it is solving the dual problem).
Bottom line: Copy and paste all the output after cvx_end into a reply.
Thanks,
Calling Mosek 9.1.9: 203188 variables, 24 equality constraints
For improved efficiency, Mosek is solving the dual problem.
MOSEK Version 9.1.9 (Build date: 2019-11-21 11:32:15)
Copyright © MOSEK ApS, Denmark. WWW: mosek.com
Platform: MACOSX/64-X86
Problem
Name :
Objective sense : min
Type : LO (linear optimization problem)
Constraints : 24
Cones : 0
Scalar variables : 203188
Matrix variables : 0
Integer variables : 0
Optimizer started.
Presolve started.
Linear dependency checker started.
Linear dependency checker terminated.
Eliminator started.
Freed constraints in eliminator : 0
Eliminator terminated.
Eliminator - tries : 1 time : 0.00
Lin. dep. - tries : 1 time : 0.01
Lin. dep. - number : 0
Presolve terminated. Time: 0.49
Problem
Name :
Objective sense : min
Type : LO (linear optimization problem)
Constraints : 24
Cones : 0
Scalar variables : 203188
Matrix variables : 0
Integer variables : 0
Optimizer - threads : 8
Optimizer - solved problem : the primal
Optimizer - Constraints : 11
Optimizer - Cones : 0
Optimizer - Scalar variables : 103188 conic : 0
Optimizer - Semi-definite variables: 0 scalarized : 0
Factor - setup time : 0.13 dense det. time : 0.00
Factor - ML order time : 0.00 GP order time : 0.00
Factor - nonzeros before factor : 66 after factor : 66
Factor - dense dim. : 0 flops : 1.12e+07
ITE PFEAS DFEAS GFEAS PRSTATUS POBJ DOBJ MU TIME
0 1.8e+05 1.8e+00 6.8e+04 0.00e+00 3.728625730e+04 0.000000000e+00 3.3e+00 0.82
1 4.5e+03 4.5e-02 1.7e+03 3.00e+00 4.708614674e+02 8.027085990e-04 8.2e-02 1.00
2 2.7e+01 2.6e-04 9.9e+00 1.02e+00 2.822202441e+00 8.112731264e-02 4.8e-04 1.04
3 1.5e+01 1.5e-04 5.5e+00 -7.89e-01 3.049452267e+00 4.696687046e-01 2.7e-04 1.09
4 4.7e+00 4.7e-05 1.8e+00 -9.29e-01 4.329623382e+00 2.148224853e+00 8.6e-05 1.14
5 4.7e+00 4.7e-05 1.8e+00 -5.16e-02 4.296255295e+00 2.143244907e+00 8.6e-05 1.17
6 1.9e+00 1.9e-05 7.0e-01 -2.19e-01 4.578020915e+00 3.618383062e+00 3.4e-05 1.22
7 1.9e+00 1.9e-05 7.0e-01 9.03e-01 4.554604478e+00 3.596599581e+00 3.4e-05 1.25
8 1.2e+00 1.2e-05 4.5e-01 8.87e-01 4.147554668e+00 3.535523134e+00 2.2e-05 1.29
9 2.8e-01 2.8e-06 1.1e-01 8.87e-01 3.809590485e+00 3.658737640e+00 5.1e-06 1.33
10 2.8e-01 2.8e-06 1.1e-01 8.05e-01 3.809590485e+00 3.658737640e+00 5.1e-06 1.36
11 2.8e-01 2.8e-06 1.0e-01 8.05e-01 3.782580544e+00 3.636950021e+00 5.1e-06 1.43
12 1.1e-01 1.1e-06 4.0e-02 8.02e-01 3.748380660e+00 3.685552365e+00 1.9e-06 1.50
13 5.7e-02 5.7e-07 2.1e-02 8.68e-01 3.738301060e+00 3.702374141e+00 1.0e-06 1.59
14 2.9e-02 2.9e-07 1.1e-02 5.92e-01 3.743240786e+00 3.720198409e+00 5.3e-07 1.69
15 2.9e-02 2.9e-07 1.1e-02 7.29e-01 3.742472145e+00 3.719859584e+00 5.2e-07 1.78
16 1.9e-02 1.9e-07 7.0e-03 6.71e-01 3.737326030e+00 3.723089594e+00 3.4e-07 1.89
17 1.3e-02 1.3e-07 4.7e-03 9.26e-01 3.735246584e+00 3.725426349e+00 2.3e-07 1.98
18 1.2e-03 1.2e-08 4.4e-04 9.57e-01 3.730618015e+00 3.729679758e+00 2.1e-08 2.08
19 1.6e-06 1.6e-11 6.1e-07 9.97e-01 3.729775464e+00 3.729774163e+00 2.9e-11 2.17
20 1.6e-10 1.5e-13 6.1e-11 1.00e+00 3.729774273e+00 3.729774273e+00 2.9e-15 2.23
21 1.9e-14 1.7e-13 5.3e-15 1.00e+00 3.729774273e+00 3.729774273e+00 2.9e-19 2.28
Basis identification started.
Primal basis identification phase started.
Primal basis identification phase terminated. Time: 0.00
Dual basis identification phase started.
Dual basis identification phase terminated. Time: 0.01
Basis identification terminated. Time: 0.08
Optimizer terminated. Time: 2.63
Interior-point solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 3.7297742729e+00 nrm: 4e+00 Viol. con: 1e-11 var: 0e+00
Dual. obj: 3.7297742729e+00 nrm: 1e+01 Viol. con: 0e+00 var: 3e-13
Basic solution summary
Problem status : PRIMAL_AND_DUAL_FEASIBLE
Solution status : OPTIMAL
Primal. obj: 3.7297742729e+00 nrm: 4e+00 Viol. con: 3e-13 var: 0e+00
Dual. obj: 3.7297742729e+00 nrm: 1e+01 Viol. con: 0e+00 var: 3e-13
Optimizer summary
Optimizer - time: 2.63
Interior-point - iterations : 21 time: 2.49
Basis identification - time: 0.08
Primal - iterations : 0 time: 0.00
Dual - iterations : 0 time: 0.01
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): -3.72977
MOSEK solves your problem in 21 iteration spending 2.63 seconds. That seems quite decent given the size of the problem and perhaps a bit slow PC.
Maybe CVX is spending a lot of time building your model. If that is the case then could try calling Mosek directly if you want to stick with Matlab.
Thanks for the answer!
Yes, you are right! I have not paid attention to this point. Most of time is used for constructing the model by MATLAB. Actually, I am generating N samples randomly using rand(1) in MATLAB and construct 3 different matrices based on some if conditions. Then, I feed these matrices to CVX.
min cost
s.t:
A1.x<=B1
A2.x<=B2
A3.x<=B3
Maybe I have to a way to construct the matrices faster! I also would welcome if you have a suggestion.
And how can I call Mosek directly in MATLAB? (As you suggested in your reply)
Best
