Portfolio Optimization MIQCP with SOC Constraint

I want to solve Portfolio Optimization problem using Benders Decomposition method, but the code is still error and I am confused to fix it because the model form is MIQCP with SOC Constraint. Does anyone can help?

Answer 1

[Aman Banthia]

Hello Sekar,

I understand that you are having errors while implementing the MALAB Code you have written.

Variable ‘z’ is not defined before using in line 47 of ‘PO_BD.m’. Assign it to the desired value and try to run the code again.

In my opinion the following code might also help you as well

clc;
tic

% Load data
Data = readtable("INPUT DATA - SEKAR.xlsx", 'ReadRowNames', true);
data = [Data.UNVR Data.ADMR Data.INKP Data.ARGO Data.SMAR Data.TFCO Data.TPIA];
[rData, cData] = size(data);

% Calculate returns
returns = diff(data) ./ data(1:end-1, :);

% Calculate mean returns
meanReturns = mean(returns);

% Calculate covariance matrix
covMatrix = cov(returns);

% Define parameters
a = 0.15 * ones(cData, 1);
b = 0.85 * ones(cData, 1);
l = zeros(cData, 1);
rho = 0.0001;

% Create optimization problems
masterProblem = optimproblem;
subProblem = cell(cData, 1);

% Define decision variables
x = optimvar('x', cData, 'LowerBound', l, 'UpperBound', b);
y = optimvar('y', cData, 'Type', 'integer', 'LowerBound', 0, 'UpperBound', 1);
t = optimvar('t', 'LowerBound', -inf, 'UpperBound', 0);

% Define master problem constraints
masterProblem.Constraints.cons1 = t <= 0;
masterProblem.Constraints.cons2 = a .* y <= x;
masterProblem.Constraints.cons3 = x <= b .* y;

% Solve subproblems and add optimality cuts to master problem
for i = 1:cData
    subProblem{i} = optimproblem;
    subProblem{i}.Objective = -t;
    subProblem{i}.Constraints.cons1 = sum(x) <= 1;
    subProblem{i}.Constraints.cons2 = -meanReturns * x <= -rho;
    subProblem{i}.Constraints.cons3 = t + norm(chol(covMatrix) * x, 2) <= 0;
    subProblem{i}.Constraints.cons4 = a(i) * y(i) <= x(i);
    subProblem{i}.Constraints.cons5 = x(i) <= b(i) * y(i);

    subObjective = subProblem{i}.Objective;
    masterProblem.Constraints.(['cons2_' num2str(i)]) = [x(i); y(i)] >= subObjective;
end

% Solve master problem
[xSol, fval] = solve(masterProblem);

% Calculate portfolio returns
portfolioReturns = returns * xSol.x;

fprintf('Optimal portfolio:\n');
disp(xSol.x);
fprintf('Objective value: %f\n', fval);

toc

Hope the above solution helps you.

Thanks,

Aman Banthia