Create the constraint that a two-element variable x must lie in the intersections of a number of disks whose centers and radii are in the arrays centers and radii.

x = optimvar('x',1,2);
centers = [1 -2;3 -4;-2 3];
radii = [6 7 8];
constr = optimineq(length(radii));
for i = 1:length(constr)
    constr(i) = sum((x - centers(i,:)).^2) <= radii(i)^2;
end

View the inequality expressions.

show(constr)

  arg_LHS <= arg_RHS

  where:

    arg1 = zeros([3, 1]);
    arg1(1) = sum((x - extraParams{1}).^2);
    arg1(2) = sum((x - extraParams{2}).^2);
    arg1(3) = sum((x - extraParams{3}).^2);
    arg_LHS = arg1(:);
    arg1 = zeros([3, 1]);
    arg1(1) = 36;
    arg1(2) = 49;
    arg1(3) = 64;
    arg_RHS = arg1(:);

    extraParams{1}:

     1    -2

  extraParams{2}:

     3    -4

  extraParams{3}:

    -2     3

Instead of using a loop, you can create the same constraints by using matrix operations on the variables.

constr2 = sum(([x;x;x] - centers).^2,2) <= radii'.^2;

Creating inequalities in a loop can be more time consuming than creating inequalities by using matrix operations.

Create indexed inequalities and variables to represent the calories consumed in a diet. Each meal has a different calorie limit. Create arrays representing the meals, foods, and calories for each food.

meals = ["breakfast","lunch","dinner"];
foods = ["cereal","oatmeal","yogurt","peanut butter sandwich","pizza","hamburger",...
    "salad","steak","casserole","ice cream"];
calories = [200,175,150,450,350,800,150,650,350,300]';

Create optimization variables representing the foods for each meal, indexed by food names and meal names.

diet = optimvar('diet',foods,meals,'LowerBound',0);

Set the inequality constraints that each meal has an upper bound on the calories in the meal.

constr = optimineq(meals);
for i = 1:3
    constr(i) = diet(:,i)'*calories <= 250*i;
end

View the inequalities for dinner.

show(constr("dinner"))

  200*diet('cereal', 'dinner') + 175*diet('oatmeal', 'dinner')
+ 150*diet('yogurt', 'dinner')
+ 450*diet('peanut butter sandwich', 'dinner') + 350*diet('pizza', 'dinner')
+ 800*diet('hamburger', 'dinner') + 150*diet('salad', 'dinner')
+ 650*diet('steak', 'dinner') + 350*diet('casserole', 'dinner')
+ 300*diet('ice cream', 'dinner') <= 750

Instead of using a loop, you can create the same inequalities by using matrix operations on the variables.

constr2 = diet'*calories <= 250*(1:3)';

Include the appropriate index names for the inequalities by setting the IndexNames property.

constr2.IndexNames = {meals, {}};

Display the new inequalities for dinner. Note that they are the same as the previous inequalities.

show(constr2("dinner"))

  200*diet('cereal', 'dinner') + 175*diet('oatmeal', 'dinner')
+ 150*diet('yogurt', 'dinner')
+ 450*diet('peanut butter sandwich', 'dinner') + 350*diet('pizza', 'dinner')
+ 800*diet('hamburger', 'dinner') + 150*diet('salad', 'dinner')
+ 650*diet('steak', 'dinner') + 350*diet('casserole', 'dinner')
+ 300*diet('ice cream', 'dinner') <= 750

Creating inequalities in a loop can be more time consuming than creating inequalities by using matrix operations.