Inequality indexing using optimization variables in MATLAB

Question

Let the variables A and B be n x 1 doubles and c be a scalar. My goal is to sum the values in A corresponding to indices for which the optimization variable x is greater than B. I have written this up below:

x = optimvar('x',n); % Creates optimization variable 
objfun = sum(x); % Creates objective function
constraint = sum(A(x>=B))>=c; % Constraint based on logical indexing

The third line in the code above returns an error message because optimization variables are not compatible with inequality indexing. Specifically, x>=B cannot be input as indexes into A. Is there a way around this? Or am I thinking about this the wrong way?

Thank you!

In optimization models, we typically use binary decision variables to model this. — Erwin Kalvelagen
– Erwin Kalvelagen, Commented Oct 9, 2020 at 2:23

Max · Accepted Answer · 2020-10-09 06:53:19Z

You need to use function handles for both, the objective function as well as the constraint-function:

objfun = @(var) sum(var); 
constraint = @(var) sum(A(var>=B)) >= c;

In fact, for the objective function objfun, you may also use objfun = @sum. This is a function handle. You can think of it as a pointer or reference to a certain function. Function, which work with one input can be used directly (with @). The optimizer calls the function and uses the optimization variable as input.

Now, if you have multiple inputs, you need to create a function, where you define all inputs but one. For this, you create an anonymous function handle, where you tell the handle what variables are placed where: @(var) sum(A(var>=B)) >= c. The variable var is the changing input and the other variables A, B, and c are taken from the workspace at the point of definition (i.e. the function handle is unaffected if you change the variables later or even delete them).

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