Existence of unique solutions in AMPL

[TasPinar204]

Dear Ladies and Gentlemen,

we are using AMPL, the AMPL API for Java and the Solver Bonmin to solve a nonlinear (quadratic) integer based problem. As stated in the theory of the optimization problem there may exist more than one solution. A question is whether it is possible that the solver gives out different solutions, when started with the same initial values several times?

Thank you for the support!
If you have any questions, don't hesitate to ask me.

Best Regards,

Pinar Tas

[svigerske]

As far as I remember, BONMIN is deterministic, so same input on same hardware should give same results, unless you use timelimits somewhere.
I don't think there is a feature build-in in BONMIN to look for "all" solutions.

[TasPinar204]

Hallo there, thank you very much. This helped me a lot! Best Regards! Pinar Tas Von: Stefan Vigerske [mailto:[email protected]] Gesendet: Mittwoch, 13. Januar 2021 03:41 An: coin-or/Bonmin Cc: Tas, Pinar (LfStat); Author Betreff: Re: [coin-or/Bonmin] Existence of unique solutions in AMPL (#17) As far as I remember, BONMIN is deterministic, so same input on same hardware should give same results, unless you use timelimits somewhere. I don't think there is a feature build-in in BONMIN to look for "all" solutions. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub<#17 (comment)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ASN7ZCGUFHC5YUIFQE5HXFDSZUB43ANCNFSM4V7C2GQQ>.

[mjsaltzman]

If you are looking for alternate solutions, one procedure is to find the first optimum, then add a constraint that rules that solution out and re-solve. You can repeat the process until the optimal objective value changes, at which point you know you have exhausted the set of optima for the original problem.

[kkofler]

But that algorithm is not reliable for nonconvex problems, which can have local optima that are not globally optimal.

[TasPinar204]

Ok thank you very much. With this information I could test it. Best Regards! Pinar Tas Von: Matthew Saltzman [mailto:[email protected]] Gesendet: Dienstag, 19. Januar 2021 16:32 An: coin-or/Bonmin Cc: Tas, Pinar (LfStat); Author Betreff: Re: [coin-or/Bonmin] Existence of unique solutions in AMPL (#17) If you are looking for alternate solutions, one procedure is to find the first optimum, then add a constraint that rules that solution out and re-solve. You can repeat the process until the optimal objective value changes, at which point you know you have exhausted the set of optima for the original problem. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub<#17 (reply in thread)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ASN7ZCFM5EAZ4OGHZLR6ZBTS2WQWVANCNFSM4V7C2GQQ>.

[TasPinar204]

Hi there, we have a convex problem. So the global optimum is equal to the local optimum. Best regards! Pinar Tas Von: Kevin Kofler [mailto:[email protected]] Gesendet: Montag, 15. Februar 2021 02:21 An: coin-or/Bonmin Cc: Tas, Pinar (LfStat); Author Betreff: Re: [coin-or/Bonmin] Existence of unique solutions in AMPL (#17) But that algorithm is not reliable for nonconvex problems, which can have local optima that are not globally optimal. — You are receiving this because you authored the thread. Reply to this email directly, view it on GitHub<#17 (reply in thread)>, or unsubscribe<https://github.com/notifications/unsubscribe-auth/ASN7ZCB3LPCZ3LG3NNCMGM3S7BZGVANCNFSM4V7C2GQQ>.