77 lines
2.1 KiB
Matlab
77 lines
2.1 KiB
Matlab
|
import gtsam.*
|
||
|
|
g = [-1; -1] % min -x1-x2
|
||
|
|
C = [-1 0
|
||
|
|
0 -1
|
||
|
|
1 2
|
||
|
|
4 2
|
||
|
|
-1 1]';
|
||
|
|
b =[0;0;4;12;1]
|
||
|
|
|
||
|
|
%% step 0
|
||
|
|
m = length(C);
|
||
|
|
active = zeros(1, m);
|
||
|
|
x0 = [0;0];
|
||
|
|
|
||
|
|
for iter = 1:2
|
||
|
|
% project -g onto the nullspace of active constraints in C to obtain the moving direction
|
||
|
|
% It boils down to solving the following constrained linear least squares
|
||
|
|
% system: min_d// || d// - d ||^2
|
||
|
|
% s.t. C*d// = 0
|
||
|
|
% where d = -g, the opposite direction of the objective's gradient vector
|
||
|
|
dgraph = GaussianFactorGraph
|
||
|
|
dgraph.push_back(JacobianFactor(1, eye(2), -g, noiseModel.Unit.Create(2)));
|
||
|
|
for i=1:m
|
||
|
|
if (active(i)==1)
|
||
|
|
ci = C(:,i);
|
||
|
|
dgraph.push_back(JacobianFactor(1, ci', 0, noiseModel.Constrained.All(1)));
|
||
|
|
end
|
||
|
|
end
|
||
|
|
d = dgraph.optimize.at(1)
|
||
|
|
|
||
|
|
% Find the bad active constraints and remove them
|
||
|
|
% TODO: FIXME Is this implementation correct?
|
||
|
|
for i=1:m
|
||
|
|
if (active(i) == 1)
|
||
|
|
ci = C(:,i);
|
||
|
|
if ci'*d < 0
|
||
|
|
active(i) = 0;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
active
|
||
|
|
|
||
|
|
% We are going to jump:
|
||
|
|
% x1 = x0 + k*d;, k>=0
|
||
|
|
% So check all inactive constraints that block the jump to find the smallest k
|
||
|
|
% ci*x1 - bi <=0
|
||
|
|
% ci*(x0 + k*d) - bi <= 0
|
||
|
|
% ci*x0-bi + ci*k*d <= 0
|
||
|
|
% - if ci*d < 0: great, no prob (-ci and d have the same direction)
|
||
|
|
% - if ci*d > 0: (-ci and d have opposite directions)
|
||
|
|
% k <= -(ci*x0 - bi)/(ci*d)
|
||
|
|
k = 100000;
|
||
|
|
newActive = -1;
|
||
|
|
for i=1:m
|
||
|
|
if active(i) == 1
|
||
|
|
continue
|
||
|
|
end
|
||
|
|
ci = C(:,i);
|
||
|
|
if ci'*d > 0
|
||
|
|
foundNewActive = true;
|
||
|
|
if k > -(ci'*x0 - b(i))/(ci'*d)
|
||
|
|
k = -(ci'*x0 - b(i))/(ci'*d);
|
||
|
|
newActive = i;
|
||
|
|
end
|
||
|
|
end
|
||
|
|
end
|
||
|
|
|
||
|
|
% If there is no blocking constraint, the problem is unbounded
|
||
|
|
if newActive == -1
|
||
|
|
disp('Unbounded')
|
||
|
|
else
|
||
|
|
% Otherwise, make the jump, and we have a new active constraint
|
||
|
|
x0 = x0 + k*d
|
||
|
|
active(newActive) = 1
|
||
|
|
end
|
||
|
|
|
||
|
|
end
|