# Minimization help in mathematica

1. Mar 25, 2009

### quantumfireball

Hi
i am finding difficulty in minimzing the following in mathematica.
Can someone try it out and share with me the results.
Its urgent.

Its a constrained minimization problem in 8 variables c2,c3....c9
Can it be tried out in matlab or maple?

NMinimize[{1.383 c2^2 + 1.377 c3^2 + 1.2618 c4^2 + 1.36 c5^2 +
1.357 c6^2 + 1.29 c7^2 + 1.35 c8^2 + 1.349 c9^2 +
2 (-0.016892 c2 c3 - 0.02962 c3 c4 - 0.01903 c3 c5 -
0.03682 c4 c5 - 0.0170 c4 c6 - 0.03789 c5 c6 +
0.0107 c3 c7 - 0.02034 c5 c7 - 0.05074 c6 c7 +
0.01112 c3 c8 + 0.01282 c4 c8 - 0.0299 c6 c8 -
0.05788 c7 c8 - 0.0275 c7 c9 - 0.0588` c8 c9),
466 < c2 < 2059, 272 < c3 < 893, 171 < c4 < 475,
116 < c5 < 288, 83 < c6 < 191, 63 < c7 < 135, 49 < c8 < 101,
40 < c9 < 78}, {c2, c3, c4, c5, c6, c7, c8, c9}]

2. Mar 26, 2009

### CompuChip

Why do you have problems with that in Mathematica?
Which version are you using?
It takes my version 6.0 only 0,25 second to produce
{465436., {c2 -> 466., c3 -> 272., c4 -> 171., c5 -> 116., c6 -> 83., c7 -> 63., c8 -> 49., c9 -> 40.}}

3. Mar 26, 2009

### quantumfireball

My dear friend i too got the same thing but are you blind to not notice that it gives only trivial values,that is the c values are just the values of the less then equality.

4. Mar 27, 2009

### CompuChip

And have you noticed yet that in each of the ci, the expression is quadratic so if the map
$$c_i \mapsto f(c_1, c_2, \cdots, c_i, \cdots, c_9)$$
where f is the expression you want to minimize, and all other values of c are fixed, has its minimum on the boundary (in particular, on the left boundary) then it is not strange that f is minimized by taking all the c on their left boundaries?

5. Mar 27, 2009

### quantumfireball

Sorry i forgot to add the following additional constraint:

c2+c3+c4+c5+c6+c7+c8+c9=2200

try it now

6. Mar 27, 2009

### CompuChip

Then I get a somewhat larger answer

{1.04414*10^6, {c2 -> 466., c3 -> 466., c4 -> 475., c5 -> 288., c6 -> 191., c7 -> 135., c8 -> 101., c9 -> 78.}}

That is still not what you want?

7. Mar 27, 2009

### quantumfireball

The soln does satisfy the constraint,but since i have included e\inequality constraints as well,why are some solutions on the boudary.Should,nt they be within in?

c1+c2+......c9=2200

Last edited: Mar 27, 2009
8. Mar 27, 2009

### CompuChip

Not necessarily. For example,

NMaximize[{x + y, 0 < x < 100, -10 < y < 10}, {x, y}]

gives x = 100, y = 10; the best way to maximize x + y is to make both variables as large as possibly allowed. If x = 100 and y = 10 is really not allowed, you should get as close as you can (e.g. x = 99, y = 9; if they must be integers).