Minimization of a integration function
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The given function is f(x)= 4+2x^2
The objective is to find the value of xa such that the following objective function is minimized.
Objective= min (int(f(x),0, xa))
Can you give me idea how to solve this in Matlab?
1 个评论
Matt J
2014-8-15
Physiker192 Commented:
why are you using an int to minimize your function? shouldn't you use the derivative??
回答（5 个）
Roger Stafford
2014-8-15
2 个投票
In general for minimization problems with constraints you should use 'fmincon'.
Roger Stafford
2014-8-15
1 个投票
There can be no finite minimum to this objective function. The more negative you make xa, the more the integral decreases. Minus infinity is the only reasonable answer. You don't need matlab to tell you that.
Image Analyst
2014-8-15
0 个投票
If xa were 0, then the integral would not cover any area and the area under the curve 4 + 2 * x^2 would be zero. That looks like it's the minimum the integral can be.
Alan Weiss
2014-8-15
fun = @(x)integral(@(t)t.*(t-2),0,x); % plot it to see how it looks
[themin,fval] = fmincon(fun,1,[],[],[],[],0,[]) % x lower bound of 0
Alan Weiss
MATLAB mathematical toolbox documentation
2 个评论
Beverly Chua
2017-10-26
Hi Alan,
I am trying to do optimization of a nonlinear objective function as well. However, my output equivalent to your "themin" above is not smooth when I try to plot it. I am trying to plot it with respect to time but it keeps spiking up and down. Is there a reason for this?
Thank you!
Alan Weiss
2017-10-26
Sorry, I do not exactly understand what you mean. It is possible that you are running into issues alluded to in Optimizing a Simulation or ODE, where an integration is a bit noisy because when you integrate over different regions the integration routine can choose different points, and that adds noise.
But I might misunderstand entirely.
Alan Weiss
MATLAB mathematical toolbox documentation
If the integrand is continuous, the unconstrained stationary points xu are those satisfying
f(xu)=0
If you add positivity constraints, a constrained local minimizer can be found by doing,
[xu,fval]=fzero(@(xu) f(xu), 0 );
if xu>=0 & abs(fval)<somethingsmall
xa= xu;
elseif xu<0 & f(0)>=0
xa=0;
else
warning 'Local min not found'
end
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2017-10-26
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