matlab实现dfp 拟牛顿法
时间: 2023-11-20 09:55:52 浏览: 50
以下是使用Matlab实现DFP拟牛顿法的示例代码:
```matlab
function [x, fval, exitflag, output] = dfp(fun, x0, options)
% fun: 目标函数句柄
% x0: 初始点
% options: 选项结构体,包含 TolFun(函数值收敛容差)、MaxIter(最大迭代次数)等参数
% 默认选项
defaultopt = struct('TolFun', 1e-6, 'MaxIter', 1000);
% 处理选项
if nargin < 3
options = [];
end
options = merge_options(defaultopt, options);
% 初始化
n = length(x0);
H = eye(n);
x = x0;
fval = feval(fun, x);
grad = gradest(fun, x);
k = 0;
% 迭代
while k < options.MaxIter
% 计算搜索方向
p = -H * grad;
% 确定步长
alpha = linesearch(fun, x, p);
% 更新x
x_new = x + alpha * p;
% 计算梯度和函数值
grad_new = gradest(fun, x_new);
fval_new = feval(fun, x_new);
% 判断收敛
if norm(fval_new - fval) < options.TolFun
exitflag = 1;
break;
end
% 更新H
s = x_new - x;
y = grad_new - grad;
H = H + (s * s') / (s' * y) - (H * y * y' * H) / (y' * H * y);
% 更新变量
x = x_new;
fval = fval_new;
grad = grad_new;
k = k + 1;
end
% 输出结果
if k == options.MaxIter
exitflag = 0;
else
exitflag = 1;
end
output.iterations = k;
output.funcCount = 2 * k + 1;
output.algorithm = 'DFP quasi-Newton method';
output.message = '';
end
function alpha = linesearch(fun, x, p)
% 一维搜索
alpha = 1;
c = 1e-4;
rho = 0.9;
fval = feval(fun, x);
grad = gradest(fun, x);
while feval(fun, x + alpha * p) > fval + c * alpha * grad' * p
alpha = rho * alpha;
end
end
function options = merge_options(defaultopt, options)
% 合并选项
if isempty(options)
options = defaultopt;
else
allfields = fieldnames(defaultopt);
for i = 1:length(allfields)
if ~isfield(options, allfields{i})
options.(allfields{i}) = defaultopt.(allfields{i});
end
end
end
end
```
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