topic Re: Optimization of function, not a model in SAS/IML Software and Matrix Computations

Optimization of function, not a model

jan_t_lagen — Fri, 09 Mar 2018 13:16:15 GMT

Hi!

I've found a model that I want to recreate for my masters thesis but the procedure is very imprecise. Essentially what I want is to find the implied probability (p) that is needed for a model to produce a certain outcome (A). In other words i want to send in some p

p = a*x + b*y where a and b are known.

So the optimization would roughly be:

1. Chose x and y

2. Calculate p and insert into the model

3. Compare result with desired outcome A

The authors just state that they use a grid search (something which i'm not familiar with) to achieve this and nothing more.

My main question is: is it possible to optimize a model like this when I'm treating the model itself as a "black box". Since the model is fairly complicated i think that if it is not possible I would try to "manually" produce code that tries a number of combinations of x and y and find the best fitted pair... although i'd prefer if there was a more elegant and simple way to achieve this.

I'm using SAS/IML.

Re: Optimization of function, not a model

Ksharp — Fri, 09 Mar 2018 14:18:45 GMT

You want P be maximize or minimize or a constant value. All these could be done vi

Re: Optimization of function, not a model

Rick_SAS — Fri, 09 Mar 2018 14:50:27 GMT

Yes, you can do this. Optimization methods don't care how the objective function is computed, and IML will compute numerical derivatives for you for any Newton-type optimizations.

Two issues that you might encounter:

1. In your example, p is the probability that depends on a and b. You will need to set constraints on a and b so that 0< p <1.

2. You don't seem to have any randomness (for example, a regression model with "noise"), but if the objective function is stochastic then the optimization algorithm will get close to the optimal value but then will "bounce around" because of the random terms.solution.)

Some articles for you to read:

Maximum likelihood estimation in SAS/IML

Optimizing a function that evaluates an integral

Optimizing a function of an integral

Re: Optimization of function, not a model

jan_t_lagen — Mon, 19 Mar 2018 13:53:18 GMT

Quick follow up question: is there a way to specify the number of iterations using "nlpnra"? I couldn't find any examples of it on the SAS forums.

It's not of great importance for me to get a perfect optimization so i would like to so how good it gets after a few step. further as there are some randomness in my objective function i fear this might make it hard to find a "perfect optimal solution"

Re: Optimization of function, not a model

Rick_SAS — Mon, 26 Mar 2018 20:40:47 GMT

Yes. By default, NLPNRA iterates as many as 200 times, but you can set the first element of the termination criteria vector to a smaller value, such as 25. (tc[1]=25)