Question

find maximum value with steepest ascent method of
f(x,y)=5+2xy+2y-x^2-2y^2 by:
a)program code(any but matlab is preferred)
b)without program code
Do 3times of iteration with initial guess is (x,y)=(0.25,0.25)

Answer 1

Hi,

Here is the required code:-

% function definition

func=@(x,y) 5+2.*x.*y +2.*y -x.^2 -2.*y.^2;

% Initial guess of x0 and y0

x0=0.25;
y0=0.25;

dx=0.001;
dy=0.001;

% initial alpha
alpha = 0.5;

%tolerance
tol =1e-6;
g = [inf;inf];

while norm(g) > tol

% compute gradient
  
f1=func(x0-dx/2,y0);
f2=func(x0+dx/2,y0);
gx=(f2-f1)/dx;
  
f1=func(x0,y0-dy/2);
f2=func(x0,y0+dy/2);
gy=(f2-f1)/dy;
g=[gx;gy];
% updating the x0 and y0 values with alpha
x0=x0+alpha*gx;
y0=y0+alpha*gy;
    
end

% displaying the value
[x0,y0]

output:-

b) Theoritical calculation:-