Question

Find points satisfying KKT neccessary conditions for the following problem 4.68; check if they are optimum points using the graphical method for two variable problem. Solve with Matlab or Excel.

4.68 Minimize f(x, x2) - 9xi - 18x,x2 + 131z - 4 subject to xi+x+2x,216 Minimize f(x,, χ-) = (x,-3)2 + (x2-3)2 4.69

Answer 1

Objective function file Matlab

41 68. Aubjed to with A2b ว่า 91 an d

function f = che(x)

f = 9* x(:,1).^2 -18*x(:,1).*x(:,2)+13*x(:,2).^2-4;

constraint function file Matlab

function [c,ceq] = con1(x)
c =-(x(1)^2 + x(2)^2+2*x(1)- 16);
ceq = [ ];

running file

options = optimoptions(@fmincon,...
'Display','iter','Algorithm','interior-point');
[x,fval] = fmincon(@con1,[3 1],...
[],[],[],[],[],[],@con1,options)

Output

Iter F-count f(x) Feasibility optimality step
0 3 -0.000000e+00 0.000e+00 8.000e+00
1 6 -3.008791e-01 0.000e+00 8.070e+00 3.633e-02
2 9 -1.360036e+02 0.000e+00 2.400e+01 8.210e+00
3 12 -3.963306e+05 0.000e+00 1.222e+03 6.172e+02
4 15 -2.496720e+10 0.000e+00 3.066e+05 1.574e+05
5 18 -3.907357e+16 0.000e+00 3.835e+08 1.975e+08
6 21 -1.526800e+24 0.000e+00 2.397e+12 1.235e+12

Problem appears unbounded.

fmincon stopped because the objective function value is less than
the default value of the objective function limit and constraints
are satisfied to within the default value of the constraint tolerance.

<stopping criteria details>

x =

1.0e+12 *

1.1987 0.2997

fval =

-1.5268e+24

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