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# Thread Subject: Optimizing Integral Equations

 Subject: Optimizing Integral Equations From: Dian Date: 5 Nov, 2012 21:00:08 Message: 1 of 3 How do I set-up an integral function where the limits are not constants so that I can optimize x.  min ( \int_{a(x)}^{b(x)} f(u) du - constant)^2   x It seems to me that quad only accepts constant limits. thanks for any help Dian
 Subject: Optimizing Integral Equations From: Roger Stafford Date: 5 Nov, 2012 21:51:08 Message: 2 of 3 "Dian" wrote in message ... > How do I set-up an integral function where the limits are not constants so that I can optimize x. > min ( \int_{a(x)}^{b(x)} f(u) du - constant)^2 > x - - - - - - - -   As I see it, your minimum will occur in one of two ways. Either it will be a zero at one or more places where your integral crosses over the "constant" value, or if this never happens, the minimum will occur at a point where f(b(x))*db(x)/dx = f(a(x))*da(x)/dx.   In the latter case the equality of these derivatives ought to be much easier to compute than continually evaluating the integral.   I am assuming here you have placed no bounds on the variable x. If you have, such bounds would also be candidates for a minimum. Roger Stafford
 Subject: Optimizing Integral Equations From: Roger Stafford Date: 5 Nov, 2012 22:30:09 Message: 3 of 3 "Dian" wrote in message ... > How do I set-up an integral function where the limits are not constants so that I can optimize x. - - - - - - - - -   An added note about terminology. It is generally understood in mathematics that an "integral equation" involves an unknown function similarly to a differential equation, rather than an unknown value of a variable. Roger Stafford