Rosen梯度投影法 matlab代码

Rosen梯度投影法是一种非线性规划优化方法，可用于求解约束条件下的最优解。以下是该算法的MATLAB实现代码：

function [x, fval] = rosen_gradient_projection(f, x0, A, b, lb, ub, maxiter, tol)
% ROSEN_GRADIENT_PROJECTION - Rosen's gradient projection algorithm for nonlinear programming
%   [X, FVAL] = ROSEN_GRADIENT_PROJECTION(F, X0, A, B, LB, UB, MAXITER, TOL) finds the minimum of
%   a nonlinear constrained function F, using the Rosen's gradient projection algorithm. X0 is the
%   initial guess, A and B are the linear inequality constraints, LB and UB are the lower and upper
%   bounds of the variables, MAXITER is the maximum number of iterations, and TOL is the tolerance
%   for the stopping criterion. The function returns the minimum X and the function value FVAL at X.

% Set default values if not specified
if nargin < 8 || isempty(tol)
    tol = 1e-6;
end
if nargin < 7 || isempty(maxiter)
    maxiter = 1000;
end
if nargin < 6 || isempty(ub)
    ub = inf(size(x0));
end
if nargin < 5 || isempty(lb)
    lb = -inf(size(x0));
end
if nargin < 4 || isempty(b)
    b = [];
end
if nargin < 3 || isempty(A)
    A = [];
end

% Initialize variables
n = length(x0);
x = x0;
fval = f(x);
g = gradient(f, x);
k = 0;

% Main loop
while k < maxiter && norm(g, inf) > tol
    % Compute the projected gradient
    gproj = project_gradient(x, g, A, b, lb, ub);

    % Compute the step size
    alpha = linesearch(f, x, gproj);

    % Update x and g
    x = x - alpha * gproj;
    fval = f(x);
    g = gradient(f, x);

    % Increment iteration counter
    k = k + 1;
end

% Display warning if maximum number of iterations reached
if k == maxiter
    warning('Maximum number of iterations reached.');
end
end

function gproj = project_gradient(x, g, A, b, lb, ub)
% PROJECT_GRADIENT - Project the gradient onto the feasible region
%   GPROJ = PROJECT_GRADIENT(X, G, A, B, LB, UB) projects the gradient G onto the feasible region
%   defined by the linear inequality constraints A*X <= B and the lower and upper bounds LB and UB.

% Compute the projection of the gradient onto the feasible region
gproj = g;
if ~isempty(A)
    gproj = gproj - A' * ((A * x - b) ./ sum(A.^2, 2))';
end
gproj(x == lb & gproj < 0) = 0;
gproj(x == ub & gproj > 0) = 0;
end

function alpha = linesearch(f, x, g)
% LINESEARCH - Compute the step size using line search
%   ALPHA = LINESEARCH(F, X, G) computes the step size ALPHA using the line search algorithm.

% Set initial values
alpha = 1;
c = 1e-4;
rho = 0.9;
f0 = f(x);
g0 = g' * g;

% Main loop
while f(x - alpha * g) > f0 - c * alpha * g0
    alpha = rho * alpha;
end
end

function g = gradient(f, x)
% GRADIENT - Compute the gradient of a function
%   G = GRADIENT(F, X) computes the gradient G of a function F at a point X.

% Set step size
h = 1e-6;

% Initialize gradient vector
g = zeros(size(x));

% Compute gradient for each variable
for i = 1:length(x)
    x1 = x;
    x1(i) = x(i) + h;
    x2 = x;
    x2(i) = x(i) - h;
    g(i) = (f(x1) - f(x2)) / (2 * h);
end
end

该代码实现了Rosen梯度投影法的主要步骤，并考虑了线性不等式约束和变量边界。您可以将自己的非线性约束函数作为输入参数f，并调整其他输入参数以满足您的问题需求。