fmincon command to find minimum value of Rosenbrock's function in Polygonal domain

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

Answer 1

[Matt J]

You have miscalculated your A and b. You can use vert2lcon to obtain them automatically,

https://www.mathworks.com/matlabcentral/fileexchange/30892-analyze-n-dimensional-polyhedra-in-terms-of-vertices-or-in-equalities

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,

[massimiliano de martino]

Thank you for your advice and support