Steepest Accent Method

Solves multivariant unconstrained optimization using the Steepest Accent Method

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