Brown Bag Seminar - March 8, 2006
Speaker: Jonathan Eckstein
Affiliation: Rutgers Business School and RUTCOR
Title: Two Optimization Problems Arising from Nonhomogeneous Poisson Processes.
Time: 12:00 - 1:00 PM
Location: RUTCOR Building - Lounge, Rutgers University, Busch Campus, Piscataway, NJ
Abstract:
Suppose we wish to monitor an information source, such as a website,
to which information is added at random times. If we are allowed a
limited number of polls in a given period, what are the best times to
place them? We model information addition as a nonhomogeneous Poisson
process, and develop a corresponding cost model. The resulting
optimization problem is very difficult to solve exactly, but may be
solved approximately by discrete-time dynamic programming, followed by
local search. We are able to bound the cost difference between the
resulting solution and the true optimum.
I will briefly discuss a possible future project: extending this
procedure to coordinated polling of multiple sources, using
branch-and-price integer programming techniques.
Time permitting, I will discuss a different but related problem:
estimating the arrival rate function of a nonhomogeneous Poisson
process from a sample of arrival times or counts. If a smooth
estimate is desired, nonnegative splines are an attractive class of
functions over which to search. We show that maximum likelihood
estimation over nonnegative splines reduces to a convex programming
problem involving linear constraints and positive semidefinite matrix
constraints. We present numerical results in which we use a
cross-validation procedure to set the number of spline knots.
Various portions of this work joint with:
Farid Alizadeh (Rutgers Business School and RUTCOR)
Avigdor Gal (Technion, formerly Rutgers Business School)
Nilay Noyan (Sabanci University, formerly RUTCOR)
Gabor Rudolf (RUTCOR)
Back to Seminars Page.
Back to RUTCOR homepage.
| 
