Page 305 - MATLAB an introduction with applications

290 ——— MATLAB: An Introduction with Applications

>> [x0_u,f0_u]=fminunc(f,x0) % MATLAB built-in fminunc
Warning: Gradient must be provided for trust-region method;
using line-search method instead.
> In fminunc at 243
Optimization terminated: relative infinity-norm of gradient less than
options.TolFun.
x0_u =
0.4867 –0.1888
f0_u =
10.5382
>> [fc_u,f0_u,c0_u]=f322p(x0_u) % its results
fc_u =
10.5382
f0_u =
8.8627
c0_u =
–0.9119
0.5161

function [fc,f,c]=f322p(x)
f=(x(1)^2+x(2)^2–6*x(1)–8*x(2)+10);
c=[–4*x(1)^2+x(2)^2; 3*x(1)+5*x(2)]; % Constraint vector
v=[1 1];e=[1 1 ]’;% Weighting coefficient vector
fc=f+v*((c>0).*exp(e.*c)); % New objective function

function [xo,fo]=opt_quad(f,x0,TolX,TolFun,MaxIter)
%search for the minimum of f(x) by quadratic approximation method
if length(x0)>2, x012=x0(1:3);
else
if length(x0)==2, a=x0(1); b=x0(2);
else a=x0–10; b=x0+10;
end
x012= [a (a+b)/2 b];
end
f012= f(x012);
[xo,fo]=opt_quad0(f,x012,f012,TolX,TolFun,MaxIter);

function [xo,fo]=opt_quad0(f,x012,f012,TolX,TolFun,k)
x0= x012(1); x1= x012(2); x2= x012(3);
f0= f012(1); f1= f012(2); f2= f012(3);
nd= [f0–f2 f1–f0 f2–f1]*[x1*x1 x2*x2 x0*x0; x1 x2 x0]’;
x3= nd(1)/2/nd(2); f3=feval(f,x3); 78ikol