Non Linear Constraint

[skyline]

Hello,

I have Non linear Constraint in my problem given by :

C4{i in N} : F[i] == Pmax / (y[i]);

F{N} Variable  such as 0=<F[i]<=Pmax
y{N} variable  such as 0=<y[i]
Pmax is a positive paramater

When I solve this problem with C4 constraint using : KnitroAmpl, Bonmin, IPOPT.

The solvers to avoid the problem of division by zero they fix the value of y[i] to 1.I get wrong results because in many cases y[i] sould be equal to zero

here is an example of the solution i get:

:    y   F     :=
1    5    2
2    1   10
3    1   10
4    1   10
5    1   10
6    1   10
7    1   10
8    1   10
9    1   10
10   1   10
;

When I should get the following :

:    y   F     :=
1    5    2
2    0   10
3    0   10
4    0   10
5    0   10
6    0   10
7    0   10
8    0   10
9    0   10
10   0   10
;

I did add a test on the value of y[i]. I changed C4 by this constraint:

C444{i in N}: F[i] = if (y[i]=0) then Pmax
else Pmax/y[i];


I get the Same results also.

Any help please. I will be very grateful.

[richar...@gmail.com]

You should be able to solve the original form of the problem using Knitro by using the Knitro "honorbnds=1" option.  This will force the variables y[i] to remain "strictly" positive throughout the optimization, though they should get asymptotically close to 0 near the solution.  Since the y[i] will never be exactly "0" though, the constraint C4 will remain well defined.

Richard Waltz
Artelys Corp

[skyline]

Hello,

Thanks for your reply.

I did use the "honorbnds=1" option you suggested.The results are the same with knitro.

  L     y

  2      5

 10     1

 10     1

 10     1

 10     1

 10     1

 10     1

 10     1

 10     1

 10     1

[Michael Saunders]

Yakine, the natural suggestion is to replace your dangerous singularity

by constraints that should be equivalent:

C4safer{i in N} : F[i]*y[i] == Pmax;

Since Pmax is positive, y[i] cannot be zero, so each y could have a positive lower bound.

(This would also safeguard your original formulation.)

Michael

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[F.YAKINE]

Hi Michael , 

Thank you very much for your reply.   I will try definitely try C4safe you suggested 

 

Best regards.

 

--

F.YAKINE