Minimize a function with equality, inequality, and product in constraints

Hello community, can anyone please help me to get the solution of this problem.

I have to minimize the following objective function:

OF= (x1+x2)*0.1– x3*0.3+ (x4+x5)*0.9-(x6+x7)*0.8

With respect to the following constraints:

X1+x2+x6= 10

X1+x3+x4=12

(x5+x2)*( x3+x7)= 0

0.1 <= (x5+x2)*10-(x3+x7)*0.9 <= 0.9

0<=x5+x2<=P3

0<=x3+x7<=P4

xLowerBound: [0 0 0 0 0 0 0]

xUpperBound: [12 4 4 12 4 10 4]

[Askic V]

Please have a loook at this part of the documentation:

https://www.mathworks.com/help/optim/ug/nonlinear-constraints.html

Answer 1

[Torsten]

x2,x3,x5 and x7 are all >= 0.

Thus the constraint (x5+x2)*(x3+x7) = 0 either gives x5=x2=0 or x3=x7=0.

Thus use "linprog" twice:

In the first run, optimize your function under the constraint x5=x2=0, in the second run, use the constraint x3=x7=0.

After these two runs, take the better of these two runs as solution.