Steepest Decent Method for Multiple Variable Functions
by Siamak Faridani
07 Jan 2009
No BSD License
Solves a multivariable unconstrained optimization method using the Steepest Decent Method
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| File Information |
| Description |
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 |
| MATLAB release |
MATLAB 7.5 (R2007b)
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| Other requirements |
You may need the Symbolic toolbox based on your MATLAB version |
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