Find minimum in one variable only

11 次查看（过去 30 天）
Erin
Erin 2018-8-8
回答： Rik 2018-8-8
I have a complicated two-variable function f(x,t), for 0 < x, t < 1.
My goal is to estimate the integral from 0 to 1 of min_{0<t<1} |f(x,t)|.
I have tried using fminbnd, but I'm having problems since the input is a function of two variables.
My initial definition of f looked like
syms x t
f = cos(x)*exp(t^2); % actual function is much more complicated than this.
Note that I do not expect to be able to locate extrema analytically.
The best I can do so far is compute the minimum at a number of x-values, like this:
d = []; % vector to hold minima
N = 100; % number of x-values to check
for j = 0 : N
f = @(t)cos(j/N)*exp(t^2);
d = [d, [fminbnd(f,0,1)]];
end;
I can then use the vector d to approximate the integral I want. However, this seems slow and inefficient. Any suggestions would be welcome.

请先登录，再回答此问题。

回答（1 个）

Rik
Rik 2018-8-8
You can use a trick to make it a single input function: use a vector.
f = @(x,t)cos(x)*exp(t^2);
B=fminbnd(@(b)f(b(1),b(2)),[0;1],[0;1]);
I use this trick often with fminsearch if I want to fit a function, but don't know if the end user has the curve fitting toolbox:
%needed input: x and yx
% Objective function (Exponential)
y = @(b,x) b(1)*exp(b(2)*x);
% Ordinary Least Squares cost function
OLS = @(b) sum((y(b,x) - yx).^2);
opts = optimset('MaxFunEvals',50000, 'MaxIter',10000);
% Use 'fminsearch' to minimise the 'OLS' function
fit_output = fminsearch(OLS, intial_b_vals, opts);

类别

在 Help Center 和 File Exchange 中查找有关 Calculus 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by