Matlab 求多变量函数的最小值
问题:在窗口[0,2]×[2,4]中找到f(x,y)=x^2+y^2-2*x-6*y+14的最小值,x和y的增量为0.01 我的方法:找到外汇和fy的一阶偏导数。临界点同时满足方程fx(x,y)=0和fy(x,y)=0。求二阶偏导数fxx(x,y)、fyy(x,y)和fxy(x,y)以求DMatlab 求多变量函数的最小值,matlab,minimum,differentiation,Matlab,Minimum,Differentiation,问题:在窗口[0,2]×[2,4]中找到f(x,y)=x^2+y^2-2*x-6*y+14的最小值,x和y的增量为0.01 我的方法:找到外汇和fy的一阶偏导数。临界点同时满足方程fx(x,y)=0和fy(x,y)=0。求二阶偏导数fxx(x,y)、fyy(x,y)和fxy(x,y)以求D clc clear all syms x y fun=x^2+y^2-2*x-6*y+14; fx=diff(fun,x); fy=diff(fun,y); pt=solve(fx==0,fy==0); so
clc
clear all
syms x y
fun=x^2+y^2-2*x-6*y+14;
fx=diff(fun,x);
fy=diff(fun,y);
pt=solve(fx==0,fy==0);
sol = struct2array(pt)
fxx=diff(fx,x);
fyy=diff(fy,y);
fxy=diff(fx,y);
D=subs(fxx,[x y],[1 3])*subs(fyy,[x y],[1 3])-(subs(fxy,[x y],[1 3]))^2
fxx_val=subs(fxx,[x y],[1 3])
minimum_value=subs(fun,[x y],[1 3])
我对问题的回答是否正确?除此之外,窗口和增量提到了这个问题。任何提示或解决方案都将不胜感激。提前感谢。使用功能评估优化方法,而不是梯度
f = @(x,y)x.^2+y.^2-2.*x-6.*y+14;
% x range
x_lb = 0;
x_ub = 2;
% y range
y_lb = 2;
y_ub = 4;
step = 0.01;
% lower bound of x, initial guess as xmin
xmin = x_lb;
% lower bound of y, initial guess as ymin
ymin = y_lb;
% f at the lower bounds, initial fmin
fmin = f(xmin, ymin);
for x = x_lb:step:x_ub
for y = y_lb:step:y_ub
% function evaluation
fval = f(x, y);
%replace fmin if the newly evaluated f is less than the actual fmin
if fval < fmin
fmin = fval;
% save current x and y where f is minimum
xmin = x;
ymin = y;
end
end
end
xmin = 1;
ymin = 3;
fmin = 4;
请通读代码
f = @(x,y)x.^2+y.^2-2.*x-6.*y+14;
% x range
x_lb = 0;
x_ub = 2;
% y range
y_lb = 2;
y_ub = 4;
step = 0.01;
% lower bound of x, initial guess as xmin
xmin = x_lb;
% lower bound of y, initial guess as ymin
ymin = y_lb;
% f at the lower bounds, initial fmin
fmin = f(xmin, ymin);
for x = x_lb:step:x_ub
for y = y_lb:step:y_ub
% function evaluation
fval = f(x, y);
%replace fmin if the newly evaluated f is less than the actual fmin
if fval < fmin
fmin = fval;
% save current x and y where f is minimum
xmin = x;
ymin = y;
end
end
end
xmin = 1;
ymin = 3;
fmin = 4;
使用函数评估优化方法代替梯度
f = @(x,y)x.^2+y.^2-2.*x-6.*y+14;
% x range
x_lb = 0;
x_ub = 2;
% y range
y_lb = 2;
y_ub = 4;
step = 0.01;
% lower bound of x, initial guess as xmin
xmin = x_lb;
% lower bound of y, initial guess as ymin
ymin = y_lb;
% f at the lower bounds, initial fmin
fmin = f(xmin, ymin);
for x = x_lb:step:x_ub
for y = y_lb:step:y_ub
% function evaluation
fval = f(x, y);
%replace fmin if the newly evaluated f is less than the actual fmin
if fval < fmin
fmin = fval;
% save current x and y where f is minimum
xmin = x;
ymin = y;
end
end
end
xmin = 1;
ymin = 3;
fmin = 4;
请通读代码
f = @(x,y)x.^2+y.^2-2.*x-6.*y+14;
% x range
x_lb = 0;
x_ub = 2;
% y range
y_lb = 2;
y_ub = 4;
step = 0.01;
% lower bound of x, initial guess as xmin
xmin = x_lb;
% lower bound of y, initial guess as ymin
ymin = y_lb;
% f at the lower bounds, initial fmin
fmin = f(xmin, ymin);
for x = x_lb:step:x_ub
for y = y_lb:step:y_ub
% function evaluation
fval = f(x, y);
%replace fmin if the newly evaluated f is less than the actual fmin
if fval < fmin
fmin = fval;
% save current x and y where f is minimum
xmin = x;
ymin = y;
end
end
end
xmin = 1;
ymin = 3;
fmin = 4;
我建议利用Matlab的能力来计算矩阵。然后,不需要循环
% your function, look up anonymous functions
func = @(x,y) x.^2 + y.^2 - 2.*x - 6.*y + 14;
% get matrices for you x- and y-window
[xg, yg] = meshgrid(0:.01:2, 2:0.01:4);
% compute all in one call
result = func(xg,yg);
% find total minimum
minimum = min(result(:));
% find the index of the (first) minimum, for other equations, there might
% be more than one
ind = find(result==minimum, 1);
% Output the result
fprintf('The minimum (%d) is located at x: %d, y: %d.\n', minimum, xg(ind), yg(ind));
我建议利用Matlab的能力来计算矩阵。然后,不需要循环
% your function, look up anonymous functions
func = @(x,y) x.^2 + y.^2 - 2.*x - 6.*y + 14;
% get matrices for you x- and y-window
[xg, yg] = meshgrid(0:.01:2, 2:0.01:4);
% compute all in one call
result = func(xg,yg);
% find total minimum
minimum = min(result(:));
% find the index of the (first) minimum, for other equations, there might
% be more than one
ind = find(result==minimum, 1);
% Output the result
fprintf('The minimum (%d) is located at x: %d, y: %d.\n', minimum, xg(ind), yg(ind));
你可以使用Matlab内置的优化工具吗?@Adam是的,先生。允许使用内置优化工具您允许使用Matlab内置优化工具吗?@Adam Yes先生。允许使用内置的优化工具,谢谢。现在我明白了窗口和增量的含义。1天后我会接受你的回答:)再次感谢汉克斯先生。现在我明白了窗口和增量的含义。1天后我会接受你的回答:)再次感谢