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,
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.
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.