Matlab Assignment 2

The problem can be summarized as: Given $y\in {\mathbb{R}}^{100}$, estimate $x\in {\mathbb{R}}^{10}$, where $y=Ax+v$, where $v$ is the error introduced by the quantization.

The task is given by

% Standard form (Hint: Standard form requires all variables to be positive. Use a similar trick as above.)
c = 
D = 
d = 
LB = 
UB = 
% zopt = linprog(c,[],[],D,d,LB,UB); % If we want, we can verify that we get the same solution
% xopt = zopt(1:nx) - zopt(nx+1:2*nx);
 
% Dual problem
[lambdaopt,fval,exitflag,output,Zopt] = linprog(,,); % Specify the three first input parameters! 

And the solution is given by

% Standard form (Hint: Standard form requires all variables to be positive. Use a similar trick as above.)
c = [zeros(1, 2*nx) ones(1, L) ones(1, L)]; % Adjust c to include x+ and x-
 
% Adjust D to include x+ and x- parts
D = [A -A eye(L) -eye(L)];
d = y; % stays the same
 
% New bounds, all non-negative
LB = zeros(1, 2*nx + 2*L); % Lower bounds
UB = []; % Upper bounds not necessary, implies infinity
 
% zopt = linprog(c,[],[],D,d,LB,UB); % If we want, we can verify that we get the same solution
% xopt = zopt(1:nx) - zopt(nx+1:2*nx);
 
% Dual problem
[lambdaopt,fval,exitflag,output,Zopt] = linprog(-d,D',c'); % Specify the three first input parameters!
xopt = Zopt.ineqlin(1:nx) - Zopt.ineqlin(nx+1:2*nx); % The optimal z is now the lagrangian multiplier of the inequality constraint
 
figure(2)
stairs(0:10,[x;x(end)]); xlabel('t'); ylabel('u(t)'); hold on;
stairs(0:10,[xopt;xopt(end)],'r--'); hold off;