Steepest Accent Method

Solves multivariant unconstrained optimization using the Steepest Accent Method

Description

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

• MATLAB release: MATLAB 7.5 (R2007b)
• Other requirements: May need symbolic toolbox based on your Matlab version

[Duc]

Run with
x01=1;
x02=2;

and

a='10*(2*x1-5)^2+2*(3*x2-6)^2';
 
then I get an error:
alphaval =
 
C_
 
??? Error using ==> evalin
Undefined function or variable 'C_'.

[Duc]

untitle4.m
function Untitled4()
syms alpha
f='alpha'
diff(f,alpha)
%error!!

untitle4p.m
syms alpha
f='alpha'
diff(f,alpha)
%get expected result

untitle5.m
function Untitled4()
syms alpha1
f='alpha1'
diff(f,alpha1)
%get expected result