Optimization giving unexpected results

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Gimpy
Gimpy 2014-8-11
评论： Gimpy 2014-8-11
Hi, I'm trying to optimize a function which I know the results but matlab is giving me weird results. Here's what I'm trying to do:
max: f(x)= 1815x1+379x2
subject to: -1475x1-112013x2 >= -700000
x1,,x2<=80
x1,x2>=0
How would you do it?
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Yu Jiang
Yu Jiang 2014-8-11
编辑：Yu Jiang 2014-8-11
Can you share your code? Which built-in function are you using?
Bear in mind that both functions fminsearch and fmincon search for the minimum not the maximum.
-Yu
Gimpy
Gimpy 2014-8-11
f = [1815;379]
A = [-1475 -11203]
b = [-700000]
ub= (ones(1,2)*80)'
lb = zeros(2,1)
x = linprog(f,A,b,[],[],lb,ub)

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Yu Jiang
Yu Jiang 2014-8-11
编辑：Yu Jiang 2014-8-11
Hi Gimpy
Since linprog finds the minimum for the function f(x) but the problem you are trying to solve is a maximization problem, I suggest you change f = [1815;379] to f = -[1815;379]. That is to say, you solve the following problem instead
min: f(x)= - 1815x1 -379x2
subject to: -1475x1-112013x2 >= -700000
x1,,x2<=80
x1,x2>=0
There will only be a sign difference on the objective function. The optimal solutions x will be the same.
-Yu
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Yu Jiang
Yu Jiang 2014-8-11
Hi Gimpy
The answer seems not correct, since -1475*40 -11203*80 = -955240 <=700000, meaning the first inequality constraint is not satisfied.
Also, linprog treats inequality constraints as "<=" by default, not ">=". So your A and b matrices should be A = [1475 11203] and b = 700000
-Yu
Gimpy
Gimpy 2014-8-11
Yes after a double check I realized it's my model that was mispecification not the matlab function that I don't understand. My understanding was correct. thank you

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