topic Re: Optmodel - "Algorithm failed to converge" in Mathematical Optimization, Discrete-Event Simulation, and OR

Optmodel - "Algorithm failed to converge"

tom12122 — Tue, 10 Sep 2013 08:17:48 GMT

Hi,

When I execute OPTMODEL procedure I get, in certain circumstances message that "Algorithm failed to converge.". What exaclty that mean? Is there a way (options: maxiter, tech ?) to somehow get successfull optimal solution? Does it mean that the problem has no solution - as far as I investigated It should have optimal solution.

I attach sample data and SAS code.

Message was edited by: tsf sfsdf

Re: Optmodel - "Algorithm failed to converge"

MichelleHomes — Tue, 10 Sep 2013 12:59:08 GMT

Hi,

As the message states an optimal solution could not be provided due to the underlying algorithm failing to converge. This could be due to the solver you have specified in your code (or from using the default solver). As you haven't provided your code it is difficult to know what it could be.

Some information on numerical difficulties and suggestions can be found in the SAS/OR user guide, SAS/OR(R) 12.3 User's Guide: Mathematical Programming As the page suggests you may also want to try a different solver and algorithm in PROC OPTMODEL using the SOLVER= option on the SOLVE statement, http://support.sas.com/documentation/cdl/en/ormpug/66107/HTML/default/viewer.htm#ormpug_optmodel_sect027.htm#ormpug.optmodel.npxsolvestmt

Other thoughts are to look at using initial values (or not) and also perhaps use a presolver.

Kind Regards,

Michelle

Re: Optmodel - "Algorithm failed to converge"

tom12122 — Fri, 13 Sep 2013 11:47:43 GMT

I attached sample SAS code and files

Re: Optmodel - "Algorithm failed to converge"

tom12122 — Wed, 09 Oct 2013 13:24:42 GMT

Can you help with this problem? Thanks

Re: Optmodel - "Algorithm failed to converge"

wezhou — Mon, 21 Oct 2013 18:25:48 GMT

We are looking at this problem, and will let you know. Thanks.

Re: Optmodel - "Algorithm failed to converge"

wezhou — Wed, 23 Oct 2013 18:11:18 GMT

We noticed that your objective has the form g1(x)/sqrt(g2(x)) where g2(x) appears to be very small when it is close to the solution. Further g2(x) is realized by summing a number of terms together. Numerical issues can occur whenever the individual terms in the summation are much larger than the cumulative result. It appears that most of the solvers we tried for your problem converge to the same point (we believe that it is an optimal solution) with the current formulation, but are unable to exit due to the optimality tolerance. One solution is to simply relax the tolerance for this problem. Alternatively, sometimes simple reformulations can improve convergence.

Attached is an equivalent variation that is quickly solved by optmodel’s nlp solver. Note that for the same attached reformulation we tried NLPC. NLPC appears to stop when the objective surpasses a given threshold for an infeasible solution. In general we suggest using the newer solvers and have found them to be more robust in the presence of general nonlinear constraints.

Attached are the new model and corresponding log file from the nlp.

Please feel free to ask if you have any new questions. Also, please feel free to use SAS’s defect track system.

http://support.sas.com/ctx/supportform//createForm

Best,

Re: Optmodel - "Algorithm failed to converge"

tom12122 — Wed, 23 Oct 2013 19:54:45 GMT

Thank you for help.

Can you tell me what option should I use in solution one - to "relax the tolerance for this problem"?

Re: Optmodel - "Algorithm failed to converge"

wezhou — Wed, 23 Oct 2013 20:15:00 GMT

You can try solver option: opttol. For example, set opttol=1.0e-4.

Re: Optmodel - "Algorithm failed to converge"

tom12122 — Wed, 23 Oct 2013 20:51:38 GMT

I'm using SAS 9.2 - is that option also available in my version?

By the way - by accident I used option "FD=CENTRAL" and it seems to cause problem to disapear - Is it just a coincidence?

Re: Optmodel - "Algorithm failed to converge"

wezhou — Wed, 23 Oct 2013 21:28:04 GMT

You may try RELOPTTOL for SAS 9.2. You can set RELOPTTOL=1.0e-4.

As to FD=CENTRAL, I cannot reproduce what you described.

Re: Optmodel - "Algorithm failed to converge"

tom12122 — Wed, 23 Oct 2013 21:41:15 GMT

Ok - I got it - i need to put it after SOLVE eg.

SOLVE WITH NLPC /TECH=QUANEW RELOPTTOL=0.00001;

Coming back to my FD=CENTRAL -

PROC OPTMODEL INITVAR PRINTLEVEL=2 FD=CENTRAL;

I get more or less the same result:

NOTE: The problem has 10 variables (0 free, 0 fixed).

NOTE: The problem has 1 linear constraints (0 LE, 1 EQ, 0 GE, 0 range).

NOTE: The problem has 10 linear constraint coefficients.

NOTE: The problem has 0 nonlinear constraints (0 LE, 0 EQ, 0 GE, 0 range).

NOTE: Using numeric derivative approximations for objective.

NOTE: Initial point was changed to be feasible to bound and linear constraints.

NOTE: The experimental quasi-Newton method with BFGS update is used.

NOTE: Optimality criteria (ABSOPTTOL=0.001, RELOPTTOL=1E-6) are satisfied.

NOTE: Objective = 0.5377052804.

NOTE: The data set WORK.OPT_STAT has 6 observations and 3 variables.

NOTE: The data set WORK.OPT_RESULT has 10 observations and 3 variables.

Re: Optmodel - "Algorithm failed to converge"

wezhou — Thu, 24 Oct 2013 15:51:18 GMT

Another thing that you can try is to multiply a number on the objective function (for example, 1.0e-3). It sometimes helps the convergence. It is mainly to do with the better scaling for the multipliers of the constraints.