![untitled.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/237763/untitled.png)
fmincon command to find minimum value of Rosenbrock's function in Polygonal domain
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massimiliano de martino
on 10 Sep 2019
Commented: massimiliano de martino
on 10 Sep 2019
Hi,
I Have a problem with fmincon command,particularly i would want to find minimum value of a function,in that case Rosenbrock's function, not in all domain,but only inside a polygonal domain which has been defined by means of Inequalty Constraint, which i've built by means of 4 points.
Particularly domain in which i would like to fine minimum value is defined by 4 straight lines as defined in the figure attached(domain).
I've realized following code,but fmincon give me as result a point which is outside this polyogon as it can be oberserved in figure attached (domain_2)
Following cose which i use:
clear
clc
close all
%% Define point-vertex of polygon
P1 = [1 3];
P2 = [2 1];
P3 = [4 1];
P4 = [5 3];
%% Plot four points which define polygon
figure(1);grid on;hold on;
plot([P1(1,1) P2(1,1)],[P1(1,2) P2(1,2)]);
plot([P2(1,1) P3(1,1)],[P2(1,2) P3(1,2)]);
plot([P3(1,1) P4(1,1)],[P3(1,2) P4(1,2)]);
plot([P4(1,1) P1(1,1)],[P4(1,2) P1(1,2)]);
hold off
%% plot streigh line which define polygon
figure(1);grid on;hold on;
scatter(P1(1,1),P1(1,2),'filled');scatter(P2(1,1),P2(1,2),'filled');
scatter(P3(1,1),P3(1,2),'filled');scatter(P4(1,1),P4(1,2),'filled');
xlim([0 6])
ylim([0 5])
hold off
%% Define streight line by means of which it has been define polygonal domain
coefficients = polyfit([P1(1,1), P2(1,1)], [P1(1,2), P2(1,2)],1);
a1 = coefficients (1);a1=abs(a1);
b1 = coefficients (2);b1=abs(b1);
%
coefficients1 = polyfit([P2(1,1), P3(1,1)], [P2(1,2), P3(1,2)],1);
a2 = coefficients1 (1);a2=abs(a2);
b2 = coefficients1 (2);b2=abs(b2);
%
coefficients2 = polyfit([P3(1,1), P4(1,1)], [P3(1,2), P4(1,2)],1);
a3 = coefficients2 (1);a3=abs(a3);
b3 = coefficients2 (2);b3=abs(b3);
%
coefficients3 = polyfit([P4(1,1), P1(1,1)], [P4(1,2), P1(1,2)],1);
a4 = coefficients3 (1);a4=abs(a4);
b4 = coefficients3 (2);b4=abs(b4);
%% Define Inequality Constraint
A = [a1 -1;a2 -1;-a3 1;-a4 1];
b = [-b1;-b2;b3;b4];
%% Define Function and starting point
fun = @(x)100*(x(2)-x(1)^2)^2 + (1-x(1))^2;
x0 = [3,2];
%%
x = fmincon(fun,x0,A,b);
%% Plot the results - which is outside polygon
figure(1);grid on;hold on;
scatter(x(1,1),x(1,2),'filled');
xlim([-5 6])
ylim([-5 5])
hold off
I hope I was clear about the issue.
Thanks in advance for your support
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Accepted Answer
Matt J
on 10 Sep 2019
Edited: Matt J
on 10 Sep 2019
You have miscalculated your A and b. You can use vert2lcon to obtain them automatically,
When I do so, I obtain
>> [A,b]=vert2lcon([P1;P2;P3;P4])
A =
-0.8944 -0.4472
0 -1.0000
0 1.0000
0.8944 -0.4472
b =
-2.2361
-1.0000
3.0000
3.1305
Substituting these into your code results in,![untitled.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/237763/untitled.png)
![untitled.png](https://www.mathworks.com/matlabcentral/answers/uploaded_files/237763/untitled.png)
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