"Trust Region Algorithm" Questions

[Gianluca_G_1]

Along this period, we have developed a calculation method that uses the Trust Region MKL API (with constraints).

We found many difficulties, but after a lot of efforts we have obtained some quite good results.

By the way, we have found also some strange behavior of your functions (eg. dtrnlspbc_solve …).

Here some question that can help us and also other users to understand the usage of this algorithm better:

1)           If we enlarge the constraints the calculation seems more stable. Maybe, the constraints work also during optimization process? In this case, the search procedure could not found some results insides the constraints range. Do you confirm this?

2)           It seems that the algorithm fails when it found minimums near the constraints. Is this problem related with the Jacobian?

3)           With same input values (initial conditions and constraints) it produces different results, sometimes very closed each other. Is it used random number generator inside the algorithm? Is this the reason?

4)           Is there any suggested criteria to setup the trust region size parameter?

5)           Is there any suggested criteria to setup the constraints?

Thank you very much

Gianluca

[Ying_H_Intel]

Hi Gianluca,

​Please  see our solve expert Alexander 's reply.

1)           If we enlarge the constraints the calculation seems more stable. Maybe, the constraints work also during optimization process?

[akalinki] That’s correct, the algorithm take into account constraints during calculation

 In this case, the search procedure could not found some results insides the constraints range. Do you confirm this?

[akalinki] Probably I didn’t catch the question…. From my best the extreme values exist inside constraint or on it. If TR have not converge in such case we need to analyze testcase on our side

2)           It seems that the algorithm fails when it found minimums near the constraints. Is this problem related with the Jacobian?

[akalinki] Cannot confirm before investigation – can we ask reproducer or log of failure?

3)           With same input values (initial conditions and constraints) it produces different results, sometimes very closed each other. Is it used random number generator inside the algorithm? Is this the reason?

[akalinki] My feeling that described situation similar to situation on picture below – the problem is nonlinear so even small changes in initial data (floating point operation) resulted in different solution

4)           Is there any suggested criteria to setup the trust region size parameter?

[akalinki] That’s hard question and it’s answer strongly depend on nonlinear problem that you want to solve. For general problem answer is no

5)           Is there any suggested criteria to setup the constraints?

[akalinki] I confused about constraint question – do you try to find any local minimum and that’s the reason why you set up constrain? In such case I recommend to play with TR without constrain and resolve issue for this functionality

 Best Regards,

Ying

[Gianluca_G_1]

We used the constraints to avoid not reasonable phisical results.

Is it possible that, If during the search "path" the algorithm goes out the constraints,  than it doesn't find the result also if it is inside these constraints?.

BR

Gianluca