Steepest Decent Method for Multiple Variable Functions

Solves a multivariable unconstrained optimization method using the Steepest Decent Method

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