Inequality Indexing using Optimization Toolbox

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Samuel L. Polk
Samuel L. Polk 2020-10-8
编辑： Matt J 2020-10-8
I would like to optimize an objective function with a constraint that is based on logical indexing. However, it seems like I can't just treat the optimization variable as I would a regular double. I was hoping for some advice about how to structure the constraint.
The code I have is written below. The variables A and B are n x 1 doubles and c is a scalar. So, I want to sum the values in A corresponding to indices for which the optimization variable x is greater than B.
x = optimvar('x',n); % Creates optimization variable
objfun = sum(x); % Creates objective function
constraint = sum(A(x>=B))>=c; % Constraint based on logical indexing
Thank you!
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Abdolkarim Mohammadi
Abdolkarim Mohammadi 2020-10-8
The error says all about it:
Unable to use a value of type optim.problemdef.OptimizationInequality as an index.
You cannot use OptimizationVariable objects for indexing. Such constraints should be defined using extra binary integer variables, so that when x>=B then the constraint is effective, and otherwise the constraint becomes redundant.

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Matt J
Matt J 2020-10-8
编辑：Matt J 2020-10-8
What Abdolkarim is getting it is the following, I believe. It requires known upper bounds U (vector or scalar) and lower bounds L on x.
x = optimvar('x',n,'Lower',L,'Upper',U);
e = optimvar('e',n,'Lower',0,'Upper',1,'type','integer');
Con.constr1 = e>=(x-B)./(U-B)/2; % x>B ==> e=1
Con.constr2 = e<=1-(B-x)./(B-L)/2; % x<B ==> e=0
Con.constr3 = A(:).'*e>=c;
prob=optimproblem('Objective',sum(x),'Constraints', Con)

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