Hi,

I would like to know if the following optimization problem has any application (or has been used to solve anything):

where is a positive constant for i=1,...,n

Thank you for your comments.

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- May 28th 2010, 12:50 PMluispipeInteresting optimization problem
Hi,

I would like to know if the following optimization problem has any application (or has been used to solve anything):

where is a positive constant for i=1,...,n

Thank you for your comments. - May 31st 2010, 07:08 AMGeoC
Looks remarkably similar to Boltzman's characterization for the distribution of the elements of a system across states , where is the probability of occupancy of state . This is subject to the constraint that . In the case of Boltzmann,

- May 31st 2010, 09:28 AMGeoC
I took a stab at this problem, and find the optimum to arise when and . Since is an arbitrary scalar, simply take and you arrive at Boltzmann's equation for H.

Thus

with - May 31st 2010, 12:09 PMSpringFan25
Certain economics problems could be expressed in this way.

If a person must spread a fixed resource (say, Time), over J activities, and the Utility derived from each activity is equal to Where is the proportion of your time that you spend doing activity k. You would maximise

The constraints would come from:

All time must be allocated

All time must be positive

It would be stupid to assume anyone had this utility function of course, but that never stopped economists before.