Optimization based line fitting

Hello!

I am using the following optimization script by which I am fitting the following curve between two points and

My question is, how can I solve the same optimization problem by adding the constraints ?

clc;
clear;

tic

%The Data: Time and response data
t = [0 10]';
y = [1 7]';
%Look at the Data
subplot(2,1,1)
plot(t,y,'*','MarkerSize',10)
grid on
xlabel('Time')
ylabel('Response')
hold on
%Curve to Fit
E = [ones(size(t)) exp(-t)]

E = 2×2

1.0000 1.0000 1.0000 0.0000

%Solving constrained linear least squares problem
% cNew = lsqlin(E,y,[],[],[1 1],y(1),[],[],[],opt) % Solver-based approach
p = optimproblem;
c = optimvar('c',2);
p.ObjectiveSense = 'minimize';
p.Objective = sum((E*c-y).^2);
% constraint example: p.Constraints.intercept = c(1) + c(2) == 0.82
sol = solve(p);

Solving problem using lsqlin.

cNew = sol.c;
tf = (0:0.1:10)';
Ef = [ones(size(tf)) exp(-tf)];
yhatc = Ef*cNew;
%plot the curve\
subplot(2,1,2)
plot(t,y,'*','MarkerSize',10)
grid on
xlabel('Time')
ylabel('Response')
hold on
plot(tf,yhatc)
title('y(t)=c_1 + c_2e^{-t}')

toc

Elapsed time is 2.581019 seconds.

[Matt J]

how can I solve the same optimization problem by adding the constraints ...?

The constraint is already satisfied by the solution that you have. What will it accomplish to formalize the constraint in the optimization?

Answer 1

[Matt J]

p = optimproblem;
c = optimvar('c',2);
p.ObjectiveSense = 'minimize';
p.Objective = sum((E*c-y).^2);
p.Constraints=[1,exp(-5)]*c>=4;
sol = solve(p);

[Simon Reclapino]

Thanks for your support. @Matt J

Could you also please help me in setting a constraint on the derivative. e.g. . However, if you'd like to, you can take a look on the detailed question in the link

https://www.mathworks.com/matlabcentral/answers/865045-how-to-put-constraints-on-the-derivative-of-a-polynomial-for-a-curve-fitting-problem?s_tid=srchtitle