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                Department of Mathematical Sciences
                   The Johns Hopkins University

               THE THIRD ANNUAL ALAN GOLDMAN LECTURE

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Patrick T. Harker                                   February 28, 2002
The Wharton School                                  304 Whitehall Hall
University of Pennsylvania                          Refreshments: 3:00 PM
                                                    Seminar: 4:00 PM

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              A GRADIENT-BASED METHOD FOR ANALYZING 
               STOCHASTIC VARIATIONAL INEQUALITIES


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                               ABSTRACT

This talk presents a method of estimating statistics of interest for 
a Stochastic Variational Inequality developed jointly with Dr. Margaret 
Belknap (U.S. Military Academy) and Dr. Chun-Hung Chen (George Mason 
University).  This method significantly reduces the heavy computational 
effort associated with generating a sample space of N solutions for N 
values of l, the vector of random variables.  Starting with a relatively 
small sample of solutions for values of l, we use the gradient information 
at those solution points to determine whether we may estimate solutions 
or must solve for actual solutions for interim values of l.  We continue 
in an iterative manner to generate a sample space of size N that consists 
of estimated solutions for some values of l and actual solutions for others.  
Using estimates in lieu of actual solutions represents significant 
computational savings.  An application to the deregulation of the U.S. natural 
gas market is used to illustrate this proposed methodology.