Optimization problem

[NataBod]

Hello, I need to solve the following problem. Have a non-linear function with many variables: y1=F(x1, x2,x3,x4). x2 variable - can take only four different values (30, ?, ?, 100). Initially x2  had array (50.50.100.100). So the problem now  is to go from (50,50, 100, 100) to (30, ?, ?, 100) and to  find  what would be ?, ?  So, i  need to change values of x2 from (50,50, 100, 100) to (30, ?, ?, 100)  while remaining other things as before.   Additional constraint is that another  function, call it Y,  for example, depends on  y1  and other variables Y = F (y1, y2, y3,,). If i change y1, then Y will  be changed too. i need that sum of Y will remain the same as if I  use (50,50,100,100). 

[ODENWALD]

Hi :

Your outline is a bit sketchy.

Are  a and b  dimensions of your array that you seek ?  Then you had an  MINLP-Problem.

Or is your  F(.)   F(x1, x2a, a,b, x2b, x3, x4)  with  x2b = 30 fixed and  x2b = 100  fixed  ?

You could Optmodel tell so.

You would use the impvar-construction and a solver presumably of type  Blackbox or LSO or  NLP.

Odenwald

[NataBod]

Hi, thank you for reply. For example,  X2- can take only 4 different values (30, ?, ?, 100). I need to find ? and ? such that sum of Z remains unchanged, but which is function of y1 (which is function of several variables )

For example,  y1= F(x1, x2, x3). And  Z= F(y1, y2, y3). initial values of X2 were 50 and 100 only. I now to use (30, ?, ?, 100) . need to go from (50,50, 100, 100) to (30, ?, ? , 100) such that total Z remains the same as before  ( can think of that as just simple constraint).  hope that would be more clear. 

X1    X2   X3 

3   30      45

4   ?        56

6   ?        54

7   100    54 

10   ?     50

3   30     45