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# Steepest Decent Method for Multiple Variable Functions (Scripts) 1.0

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• License: Freeware
• Last update: 6 years ago
• Total downloads: 158
• Price: Free |
• Operating system: Linux, Mac OS X, Win All, BSD, Solaris
• Publisher: Siamak Faridani (2 other programs)
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## Steepest Decent Method for Multiple Variable Functions (Scripts) Publisher's description

### Replace your function in the code and the output will be similar to the following

Replace your function in the code and the output will be similar to the following

Steepest Descent Method
=============
Function = -(3*x1+x2+6*x1*x2-2*(x1^2)+2*(x2^2))
Hessian......

[ 4 -6]
[ ]
[-6 -4]
Gradient......

[-3 - 6 x2 + 4 x1]
[ ]
[-1 - 6 x1 - 4 x2]
Eigen Values
[ 2*13^(1/2), 0]
[ 0, -2*13^(1/2)]

f(x0)=5.000000
_________________________________________
Iteration = 1
Gradient of X0
-7
5

X0 =
-1
0

X0 - alpha. gradient(X0) =
-1+7*alpha
-5*alpha

f(X0 - alpha. gradient(X0)) =
3-16*alpha+30*(-1+7*alpha)*alpha+2*(-1+7*alpha)^2-50*alpha^2

diff(f(X0 - alpha. gradient(X0)))/diff alpha =
-74+516*alpha

alphaval =

37/258

alphaval2 =

0.143410852713178

x1 =
0.003875968992248
-0.717054263565892

f(x2)=-0.306202
_________________________________________
Iteration = 2
Gradient of X1
1.317829457364341
1.844961240310078

X1 =
0.003875968992248
-0.717054263565892

X1 - alpha. gradient(X1) =
1/258-170/129*alpha
-185/258-238/129*alpha

f(X1 - alpha. gradient(X1)) =
91/129+748/129*alpha-6*(1/258-170/129*alpha)*(-185/258-238/129*alpha)+2*(1/258-170/129*alpha)^2-2*(-185/258-238/129*alpha)^2

diff(f(X1 - alpha. gradient(X1)))/diff alpha =
-85544/16641-4624/129*alpha

alphaval =

-37/258

alphaval2 =

-0.143410852713178

#### System Requirements:

MATLAB 7.5 (R2007b)
Program Release Status: New Release
Program Install Support: Install and Uninstall

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