ismember is used to constrain an sdpvar object to be selected from a set of constants, or to be inside MPT polytopes.


F = ismember(x,Y)


To constrain a scalar sdpvar variable to take a value from a finite set, ismember can be used.

sdpvar x
F = ismember(x,[1 2 3 4]);

Of course, this can also be obtained with a standard integer variable

intvar x
F = [1 <= x <=4];

or an integrality constraint.

sdpvar x
F = [integer(x), 1 <= x <= 4];

The functionality is more useful when the set is more complicated.

sdpvar x
F = ismember(x,[1 pi 12 -8]);

The function can also be used together with the polytope object in MPT to constrain a variable to be inside at least one of several polytopes.

x = sdpvar(3,1);
P1 = polytope(randn(10,3),rand(10,1));
P2 = polytope(randn(10,3),rand(10,1));
F = ismember(x,[P1 P2]);


Note that ismember will introduce binary variables if the cardinality of the set Y is larger than 1