linprog and ode45

Dear All,

I am solving a linear program (LP) within the right hand side function of ode45. The linear system has about 200 equality constraints. Compare to my previous solution method, without linprog.m inside the right hand side function, I am seeing a dramatic slow down in my code...

Do you know if there is a way to accelerate the performance of linprog or is it just not possible to solve LPs any faster?

Also, when I surpress the output of the linprog.m using option, the call to the options function is quite slow too...

Sincerely,

Tae

[Matt J]

Compare to my previous solution method, without linprog.m inside the right hand side function, I am seeing a dramatic slow down in my code...

Removing processing steps from code always makes the code faster and adding processing steps always slows it down.

[Matt J]

Also, when I surpress the output of the linprog.m using option, the call to the options function is quite slow too..

It's not clear why that would matter. You should only be calling optimoptions once, assuming you want the output suppressed all the time.

[Taehun Kim]

Thanks Matt! I am calling linprog.m inside the right hand side function and the LP gets solved whenever the integrator evaluates the right hand side function... So, the LP is getting solved many times...

[Torsten]

@Taehun Kim

Be careful that you don't get discontinuities into the RHS of the ODE by solving an optimization problem therein.

[Matt J]

So, the LP is getting solved many times...

Yes, but that doesn't mean you need to be repeatedly setting the optimoptions. Set them once and reuse the optionoptions object.

[Taehun Kim]

Dear Matt! Thanks, I see the point now! I will put the option into a structure as a field and I will call it each time! Yes, Dear Torsten, thanks a lot for the careful remark. Does it have to do with Lipschitz continuity? Why thes ODE solvers have hard time with the discontinuities? Thanks!!!

[Torsten]

Why thes ODE solvers have hard time with the discontinuities?

Because the numerical methods used (especially the error estimators) assume that the functions of the right-hand side are smooth.

[Taehun Kim]

I see. Thanks for the answer Torsten! It is quite helpful!

[Matt J]

Because the numerical methods used (especially the error estimators) assume that the functions of the right-hand side are smooth.

Do they? I find it hard to imagine they couldn't handle a step input, given how common those are in engineering applications of ODEs.

[Torsten]

Engineers are optimistic people ...

I had to smile when I recently saw a book titled "Numerical methods for engineers and scientists".