basics.m

%% 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