How to solve the optimization problem where constraint is calculated thorough the loop?

I have a matlab code which contains loop and has a structure similar to following (ignore the syntax). I am trying to use matlab optimization toolbox to minimize the objective_funtion. The problem I am facing is defining the constraint. It seems that the matlab optimization toolbox doesn't allow constraint variable to be calculated through the loop. How do I solve problem like this?

% optimization variables
a % it is the array of data with hourly resolution
b
c


% Loop to calculate constraint variables
for i=1:length(a)
	%%% here some calculation is done using a, b, and c
    if (Certain Condition) satisfies
	    calculation(i) = funtion1(a, b, c, other variables)
    else
        calculation(i) = funtion2(a, b, c, other variables)
   
	...
	...
	sum_calculation = sum(calculation);
end

objective_funtion = funtion3(a,b,c, other variables including sum_calculaiton)

cosntraint = sum_calculation>= 4000

Answer 1

[Sudarsanan A K]

Hi Anup,

When dealing with optimization problems in MATLAB, especially with constraints that depend on calculations within a loop, the key is to encapsulate your loop and any dependent calculations within a function that can be passed to the optimization solver as a constraint. MATLAB's optimization toolbox solvers, such as "fmincon", allow you to define both equality and inequality constraints through function handles that return the values of those constraints.

Here is a simple example where we aim to minimize a quadratic objective function subject to a constraint that involves a sum calculated in a loop:

• Set up and call the optimization solver.

% Initial guesses for a and b
initialGuess = [0, 0];

% No linear inequality or equality constraints
A = [];
b = [];
Aeq = [];
beq = [];

% No bounds
lb = [];
ub = [];

% Options
options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm', 'sqp');

% Solve
[x, fval] = fmincon(@objectiveFunction, initialGuess, A, b, Aeq, beq, lb, ub, @constraintFunction, options);

 Iter  Func-count            Fval   Feasibility   Step Length       Norm of   First-order  
                                                                       step    optimality
    0           3    0.000000e+00     4.000e+02     1.000e+00     0.000e+00     1.490e-08  
    1           6    3.200000e+02     0.000e+00     1.000e+00     1.789e+01     1.600e+01  
    2           9    3.200000e+02     5.684e-14     1.000e+00     4.553e-07     5.638e-07  

Local minimum found that satisfies the constraints.

Optimization completed because the objective function is non-decreasing in 
feasible directions, to within the value of the optimality tolerance,
and constraints are satisfied to within the value of the constraint tolerance.

% Display the optimized variables and objective function value
disp(['Optimized a: ', num2str(x(1))]);

Optimized a: 8

disp(['Optimized b: ', num2str(x(2))]);

Optimized b: 16

disp(['Minimum objective function value: ', num2str(fval)]);

Minimum objective function value: 320

• Create the objective function "objectiveFunction" (e.g., ):

function obj = objectiveFunction(x)
    % x is a vector where x(1) = a and x(2) = b
    a = x(1);
    b = x(2);
    
    % Objective function
    obj = a^2 + b^2;
end

• Create the constraint function "constraintFunction" (The constraint will be that the sum of over iterations is greater than or equal to ):

function [c, ceq] = constraintFunction(x)
    a = x(1);
    b = x(2);
    
    % Initialize the sum calculation
    sumCalculation = 0;
    
    % Example loop that could represent more complex calculations
    for i = 1:10
        sumCalculation = sumCalculation + (a + 2*b);
    end
    
    % Inequality constraint (should be <= 0 to be satisfied)
    c = 400 - sumCalculation;  % This constraint expects sumCalculation >= 400 for satisfaction
    
    % No equality constraints
    ceq = [];
end

This example demonstrates how to set up and solve a constrained optimization problem in MATLAB, where the constraint involves calculations that are represented by a loop.

For more information about the "fmilncon" function, refer to this documentation link:

https://www.mathworks.com/help/optim/ug/fmincon.html

For understanding the use-cases of anonymous functions, refer to this resource:

https://www.mathworks.com/help/matlab/matlab_prog/anonymous-functions.html

I hope this helps!

[Anup]

Hi @Sudarsanan A K, Thank you for the response. I have edited the problem above. In my code here, there are lots of conditional statements just like the edited code above. Apparantly, I now think that the problem is not the loop but the conditional statements present inside of the loop. Is there a way to address this?