Currently I am working project on the derivative of free optimization methods. however, I want find practical problem that solved using this method. So, how can I get solve practical examples using derivative free method? Please if you can, help me soon. Thanks in advance.
Best regards, Yohannes
I must confess, this is not derivative free, because derivatives make life easier.
From what I gather, you want to optimize an area given certain factors. Let’s assume you were given a property that bordered a building, you would like to get the most sqft given x amount of fence.
First thing we need to do is turn this into a math problem. We know two things about squares. That the area A=LW, and the perimeter = 2L+2W. given we only have 3 sides to our area in question, we assume that P= 2L+W. let’s assign X and Y instead. Say we have 100 feet of fencing
P=2X+Y; 100=2X+Y. let’s solve for Y 100=2X+Y 100-2X=2X+Y-2X Y=100-2x
Now plug that unto our F(a) function, A=XY =X(100-2x) =100-2x² =-2x²+100x F’(a) = 2(-2)x2-1+1(100)x1-1) =-4x+100=0 Solve for x we get: -4x+100=0 -4x100-100=0-100 -4x=-100 (-4x/-4)=(-100/-4) X=25 Now we plug this back into the original formula P=2(25)+Y 100=2(*25)+y, 100=50+y, y=50, Now we know X= 25, and y = 50m so A=XY = (25)(50) = 1,250 sqft
http://tutorial.math.lamar.edu/Classes/CalcI/Optimization.aspx