Steepest Accent Method
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For more information refer to "Nonlinear Programming: Theory and Algorithms" by by Mokhtar S. Bazaraa , Hanif D. Sherali , C. M. Shetty
Here is the sample output
Steepest Accent 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
引用
Siamak Faridani (2024). Steepest Accent Method (https://www.mathworks.com/matlabcentral/fileexchange/22640-steepest-accent-method), MATLAB Central File Exchange. 取得済み .
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