fmincon is not working

I'm trying to optimize the weights of a stock portfolio to maximize returns. I checked if expected_returns is a vector, and it is, but I still get the error message :

Error using fmincon (line 504)

Supplied objective function must return a scalar value.

Error in igggg (line 7652)

[weights, fval] = fmincon(objective, w0, A, b, Aeq, beq, lb, ub, nonlincon, options);

% Risk limits L
risk_limits = [0.02, 0.015, 0.01];
% Number of assets
num_assets = length(expected_returns);

Unrecognized function or variable 'expected_returns'.

% Run optimization for each L
for L = risk_limits
    % Objective function: maximize expected return (minimize negative return)
    objective = @(w) -sum(w .* expected_returns);
    % Constraints:
    % - Portfolio standard deviation <= L
    % - Sum of weights = 1
    A = [];
    b = [];
    Aeq = ones(1, num_assets); % Sum of weights = 1
    beq = 1;
    lb = zeros(num_assets, 1); % Weights >= 0
    ub = ones(num_assets, 1); % Weights <= 1
    
    % Nonlinear constraint: portfolio standard deviation <= L
    nonlincon = @(w) deal([], sqrt(w' * cov_matrix * w) - L);
    
    % Initial guess (equal weights)
    w0 = ones(num_assets, 1) / num_assets;
    
    % Solve optimization problem
    options = optimoptions('fmincon', 'Display', 'iter', 'Algorithm', 'sqp');
    [weights, fval] = fmincon(objective, w0, A, b, Aeq, beq, lb, ub, nonlincon, options);
end

[Torsten]

Be careful:

Your nonlinear constraint as implemented is

w' * cov_matrix * w = L^2

not

w' * cov_matrix * w <= L^2

Answer 1

[Walter Roberson]

I bet expected_returns is a row vector.

fmincon() passes values to the objective function in the shape of the x0 array. Here your x0 is w0, which is ones(num_assets,1) so it is a column vector that will be passed to the objective function.

If the objective function is passed a column vector and exxpected_returns is a row vector, then w.*expected_returns would be column vector .* row vector, which would give a 2D result. sum() of a 2D result would be a vector.