isoutside

isoutside creates a big-M model to avoid a region specified by linear inequalities.

Syntax

Model = isoutside(P)

Example

The following code finds the vertex/point on facet closest to the origin in a polytope by solving a non-convex problem involving an avoidance constraint. Note the required explicit bounds, as the model is constructed using big-M strategies.

x = sdpvar(2,1);
A = randn(10,2);
b = 10*rand(10,1);

Model = isoutside(A*x <= b)

optimize([Model, -100 <= x <= 100],x'*x)
clf
plot(A*x <= b,[],[],[],sdpsettings('plot.shade',0.1));
hold on;grid on
plot(value(x(1)),value(x(2)),'*')
r = sqrt(value(x'*x));
t = 0:0.01:2*pi;
plot(r*cos(t),r*sin(t),'--')

Comments

Note that isoutside will introduce binary variables.