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May 3, 2021 15:08
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%% Always start by clearing the internals | |
yalmip('clear') | |
% Define variables | |
x = sdpvar(10,1); | |
% Define constraints | |
Constraints = [sum(x) <= 10, x(1) == 0, 0.5 <= x(2) <= 1.5]; | |
for i = 1 : 7 | |
Constraints = [Constraints, x(i) + x(i+1) <= x(i+2) + x(i+3)]; | |
end | |
% Define an objective | |
Objective = x'*x+norm(x,1); | |
% Set some options for YALMIP and solver | |
options = sdpsettings('verbose',1,'solver','quadprog','quadprog.maxiter',100); | |
% Solve the problem | |
sol = optimize(Constraints,Objective,options); | |
% Analyze error flags | |
if sol.problem == 0 | |
% Extract and display value | |
solution = value(x) | |
else | |
display('Hmm, something went wrong!'); | |
sol.info | |
yalmiperror(sol.problem) | |
end | |
%% YALMIPs symbolic variable | |
P = sdpvar(3,3,'full') | |
x = sdpvar(3,1); | |
D = diag(x) ; % Diagonal matrix | |
H = hankel(x); % Hankel matrix | |
T = toeplitz(x); % Hankel matrix | |
x = sdpvar(1,1); y = sdpvar(1,1); | |
x = sdpvar(1); y = sdpvar(1); | |
sdpvar x y | |
P = sdpvar(3,3) + diag(sdpvar(3,1)); | |
X = [P P;P eye(length(P))] + 2*trace(P); | |
Y = X + sum(sum(P*rand(length(P)))) + P(end,end)+hankel(X(:,1)); | |
X | |
% Cells and nd-arrays | |
clear X | |
for i = 1:5 | |
X{i} = sdpvar(2,3); | |
end | |
X = sdpvar([2 2 2 2 2],[3 3 3 3 3]); | |
X = sdpvar(2,3,5); | |
Y = sum(X,3) | |
X(:,:,2) | |
X = sdpvar(2,2,2,2,'full'); | |
%% Constraints | |
n = 3; | |
P = sdpvar(n,n); | |
C = [P>=0] | |
P = sdpvar(n,n); | |
C = [P(:)>=0] | |
C = [triu(P)>=0] | |
C = [P(find(triu(ones(n))))>=0]; | |
P = sdpvar(n,2*n); | |
C = [P>=0] | |
P = sdpvar(n,n,'full'); | |
C = [P>=0]; | |
P = sdpvar(n,n); | |
C = [P>=0] + [P(1,1)>=2]; | |
C = [P>=0, P(1,1)>=2]; | |
C = [P>=0, P(1,1)<=2, sum(sum(P))==10] | |
F = [0 <= P(1,1) <= 2]; | |
my_tolerance_for_strict = 1e-5; | |
F = [0 <= P(1,1) <= 2-my_tolerance_for_strict]; | |
F = [0 <= P(1,1) <= 2]; | |
for i = 2:n-1 | |
F = [F, P(i,1) <= P(2,i) - P(i,i)]; | |
end |
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