build a sequential quadratic programming solver in matlab

main.m
% Objective function
f = @(x) x(1)^2 +x(2)^2; 

% Initial guess
x0 = [10; 12];

% Linear equality constraint
Aeq = [-3, 1]

beq = 5;

% Linear inequality constraint
A = [1, 2]

b = 10;
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main.m
% Objective function for SQP
sqpObj = @(x) f(x);

% Non-linear constraint
sqpNonlinCon = [];

% Objective gradient for SQP
sqpObjGrad = @(x) [2*x(1); 2*x(2)];

% Constraint gradient for SQP
sqpNonlinConGrad = [];

% SQP algorithm
options = optimoptions('fmincon',..., 
  'Algorithm','sqp',...
  'Display','final-detailed');
[xstar, fstar] = fmincon(sqpObj, x0, A, b, Aeq, beq, [], [], sqpNonlinCon, options)
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main.m
% Display final results
fprintf('**** SQP Solver via MATLAB ****\n');
fprintf('Optimization completed with status: %s\n', result.solver.status);
fprintf('Optimal solution: x1=%.4f, x2=%.4f\n', xstar(1), xstar(2));
fprintf('Optimal value of the objective function: %.4f\n\n', fstar);

% Plot the constraints and the optimum
[X,Y] = meshgrid(-30:.1:30,-30:.1:30);
Z = X.^2 + Y.^2;
hold on;
contour(X,Y,Z,20);
line([5,-5],[-30,30],'Color','black','LineWidth',1);
line([1,-40],[-20,10],'Color','black','LineWidth',1);
plot(xstar(1), xstar(2), 'r*');
hold off;
xlabel('X1');ylabel('X2');
title('SQP Solver - Constrained Optimization');
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