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Subject: Minimization of integral problem
Date: Sun, 20 Mar 2011 13:19:04 +0000 (UTC)
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Hello!

I am just about to solve the following minimization problem with equality and inequality constrains:

min -int_{-\inf}^{\inf} log(1+ a * f(x)) dx

s.t. f(x) >= 0, int_{-\inf}^{\inf} f(x) dx = C, int_{-\inf}^{\inf} f(x) * b(x) >= d *C

f(x) and b(x), respectively, are scalar function of x, a, C and d can be considered as constants. The optimization parameter is f(x)  What's the best way to tackle such a problem? I would have started using fmincon, but I am not sure whether this can be used because of the infinite integrals. 

What integral solver should be employed for this purpose? According to the Matlab reference quadgk seems to be the right choice ...

Any hints appreciated!