外点罚函数法matlab程序

以下是外点罚函数法的MATLAB程序示例：

function [x,fval,iter] = penalty(fun,x0,options)
% Penalty function method for constrained optimization
% fun: objective function
% x0: initial point
% options: structure with options (see documentation for optimoptions)
% x: solution
% fval: objective function value at solution
% iter: number of iterations

% Define default options if none are provided
if nargin < 3
    options = optimoptions(@fmincon,'Display','off');
end

% Define penalty function
penaltyFun = @(x) penaltyFunHelper(x,fun);

% Initialize penalty parameter and iteration counter
mu = 1;
iter = 0;

% Loop until convergence or maximum number of iterations reached
while true
    
    % Define constraint function with current penalty parameter
    cFun = @(x) penaltyFun(x) + mu * sum(max(0, -fun(x)));
    
    % Solve constrained optimization problem
    [x,fval,exitflag] = fmincon(cFun,x0,[],[],[],[],[],[],[],options);
    
    % Increment iteration counter
    iter = iter + 1;
    
    % If solution is feasible (i.e., all constraints are satisfied), return
    % solution and objective function value
    if all(fun(x) <= 0)
        return
    end
    
    % Increase penalty parameter for next iteration
    mu = mu * 10;
    
    % If exitflag is not 1 (i.e., optimization did not converge), print
    % warning message
    if exitflag ~= 1
        warning('Optimization did not converge in iteration %d',iter);
    end
    
end

end

function [f,grad] = penaltyFunHelper(x,fun)
% Helper function to compute penalty function and gradient
f = sum(max(0,fun(x)));
if nargout > 1
    grad = zeros(size(x));
    for i = 1:length(x)
        if fun(x(i)) > 0
            grad(i) = sum(max(0,fun(x)));
        end
    end
end
end

此程序实现了外点罚函数法的基本步骤。首先，定义了一个罚函数，它是原始目标函数和约束的组合。然后，使用fmincon函数求解约束优化问题，并将罚函数作为约束函数传递。如果解是可行的（即所有约束都满足），则程序返回解和目标函数值。否则，程序增加罚函数参数，并继续迭代，直到解决方案是可行的或达到最大迭代次数。