Turn on suggestions

Auto-suggest helps you quickly narrow down your search results by suggesting possible matches as you type.

Showing results for

- Home
- /
- Programming
- /
- Programming
- /
- how do I find the minimizer value in non linear optimization problem?

Options

- RSS Feed
- Mark Topic as New
- Mark Topic as Read
- Float this Topic for Current User
- Bookmark
- Subscribe
- Mute
- Printer Friendly Page

🔒 This topic is **solved** and **locked**.
Need further help from the community? Please
sign in and ask a **new** question.

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Posted 10-06-2019 05:52 PM
(868 views)

Hi,

I am trying to solve the following question

I have written the following code for this

proc optmodel; var x, y,z; min f = 4*(x^2+y-z)^2 + 10; /* starting point */ x = 1; y = 1; z=1; solve; print x y z x.dual y.dual z.dual; quit;

Now if P is the descent direction of f at Xo then

I need to find the minimizer Aplha for this problem

I mean to say that I am trying to solve this question:

I dont see Alpha in the output.

Please can someone help me find the value of Alpha which is the minimizer

thanks

1 ACCEPTED SOLUTION

Accepted Solutions

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

To find the descent direction from the initial point, you need to fix the values of the variables and then take the negative gradient. To find the best step size alpha in that direction, you can solve an auxiliary one-variable problem. The following code implements these ideas, where I have renamed the original variables x[1], x[2], and x[3].

```
proc optmodel;
num n = 3;
var x {1..n} init 1;
min f = 4*(x[1]^2+x[2]-x[3])^2 + 10;
fix x;
solve;
print x x.dual;
num p {1..n};
for {j in 1..n} p[j] = -x[j].dual;
var alpha >= 0;
min g = 4*((x[1]+alpha*p[1])^2+(x[2]+alpha*p[2])-(x[3]+alpha*p[3]))^2 + 10;
solve;
print alpha;
quit;
```

5 REPLIES 5

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Post it at OR forum . @RobPratt is there .

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

To find the descent direction from the initial point, you need to fix the values of the variables and then take the negative gradient. To find the best step size alpha in that direction, you can solve an auxiliary one-variable problem. The following code implements these ideas, where I have renamed the original variables x[1], x[2], and x[3].

```
proc optmodel;
num n = 3;
var x {1..n} init 1;
min f = 4*(x[1]^2+x[2]-x[3])^2 + 10;
fix x;
solve;
print x x.dual;
num p {1..n};
for {j in 1..n} p[j] = -x[j].dual;
var alpha >= 0;
min g = 4*((x[1]+alpha*p[1])^2+(x[2]+alpha*p[2])-(x[3]+alpha*p[3]))^2 + 10;
solve;
print alpha;
quit;
```

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

thank you so much for your answer . @RobPratt

Just one more question.I am trying to re write your program for the following problem.

min f = (x[1]-2)**4 + (x[1]-2*x[2])**2;

Sorry I am new to sas .Please can you help me write the same code as that in your answer for this new problem to calculate alpha.I tried but each time I tried I got alpah=0 and a an error message also

Thanks

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

Here's how I would do it:

```
proc optmodel;
num n = 2;
var x {1..n};
min f = (x[1]-2)**4 + (x[1]-2*x[2])**2;
fix x[1] = 0;
fix x[2] = 3;
solve;
print x x.dual;
num p {1..n};
for {j in 1..n} p[j] = -x[j].dual;
var alpha >= 0;
min g = (x[1]+alpha*p[1]-2)**4 + (x[1]+alpha*p[1]-2*(x[2]+alpha*p[2]))**2;
solve;
print alpha;
quit;
```

- Mark as New
- Bookmark
- Subscribe
- Mute
- RSS Feed
- Permalink
- Report Inappropriate Content

thank you so much

Are you ready for the spotlight? We're accepting content ideas for **SAS Innovate 2025** to be held May 6-9 in Orlando, FL. The call is **open **until September 25. Read more here about **why** you should contribute and **what is in it** for you!

How to Concatenate Values

Learn how use the CAT functions in SAS to join values from multiple variables into a single value.

Find more tutorials on the SAS Users YouTube channel.