what is the algorithm for sqp in matlab in matlab

The Sequential Quadratic Programming (SQP) algorithm is commonly used for solving constrained optimization problems. In MATLAB, you can use the fmincon function with the Algorithm option set to 'sqp' to implement the SQP algorithm.

Here is an example of how to use the SQP algorithm in MATLAB:

main.m
% Define the objective function
fun = @(x) x(1)^2 + x(2)^2;

% Define the constraints
A = [1, 2];       % Coefficients of inequality constraints
b = 3;            % Right-hand side of inequality constraints
Aeq = [3, 4];     % Coefficients of equality constraints
beq = 5;          % Right-hand side of equality constraints
lb = [-Inf, -Inf];% Lower bounds on design variables
ub = [Inf, Inf];  % Upper bounds on design variables

% Initialize the design variable
x0 = [0, 0];      % Initial guess for the design variables

% Solve the optimization problem using SQP algorithm
options = optimoptions('fmincon', 'Algorithm', 'sqp');
[x, fval, exitflag] = fmincon(fun, x0, A, b, Aeq, beq, lb, ub, [], options);

% Display the results
disp('Optimal design variables:');
disp(x);
disp('Optimal objective function value:');
disp(fval);
disp('Exit flag:');
disp(exitflag);
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In this example, the objective function is x(1)^2 + x(2)^2, and the constraints are A*x <= b and Aeq*x = beq. The design variables x are bounded by lb and ub in this case.

Note that the fmincon function requires the Optimization Toolbox in MATLAB, so make sure you have it installed.

I hope this helps you to implement the SQP algorithm in MATLAB!

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