Page 309 - MATLAB an introduction with applications

294 ——— MATLAB: An Introduction with Applications

Solution:
First we create an .m file to hold the function
function f=fx(x)
f=–(8*sin(x)–x^2/14)
The negative sign is for minimization.
>> x=fminbnd(‘fx’, 0,7)
The result from MATLAB program is
f =
–7.8268
x =
1.5432

2
2
Example E5.14: Use the MATLAB fminsearch function to find the maximum of f (x, y) = 3xy + 8x – x – 9y ,
using initial guesses, x = –1 and y = 1.
Solution:
Create an m file to hold the function
function f=fxy(x)
f=–(3*x(1)*x(2)+8*x(1)–x(1)^2–9*x(2)^2)
Invoke the fminsearch function with

>> x=fminsearch(‘fxy’,[–1,1])
f =
–21.3333
x =
5.3334 0.8889

Examples E5.15 to E5.20 are based on Tutorials and Demos from MATLAB (The Mathworks, Inc.)
Example E5.15: This is an unconstrained minimization example. Find the set of values [x , x ] that solve
2
1
min ( ) x = e 1 x (4x + 2x + 4x x + 2x + 0.9)
2
2
f
x 1 2 1 2 2
0
Starting guess: x = [–1, 1].
Solution:
MATLAB Solution [Using built-in function]:
Write an m-file objfun.m
function f=objfun(x)
f=exp(x(1))*(4*x(1)^2+2*x(2)^2+4*x(1)*x(2)+2*x(2)+0.9);

Write one of the unconstrained optimization routines:
>> x0=[–1,1]; % Starting guess at the solution
>> options=optimset(‘LargeScale’, ‘off’);
>> [x,fval,exitflag,output]=fminunc(@objfun,x0,options)