Talk Abstract:

Optimization of Uncertain Dynamic Systems: Partial Differential Equation Systems for Groundwater Contamination

Christine Shoemaker
School of Civil and Environmental Engineering and Center for Applied Mathematics
Cornell University
cas12@cornell.edu

This talk will discuss the application of nonlinear optimization to systems described by partial differential equations. The system to be optimized is a contaminated groundwater aquifer and the decision variables are the location of well and the rates of pumping to extract or inject water into the aquifer at each of the wells. The objective is to minimize cost of clean up and the constraints on the maximum allowable concentration of contaminant at the end of the clean-up period. This is a huge nonlinear optimization problem since the partial differential equations must be solved by finite element procedures, with the result that there are thousands of variables in each time step. Stochastic dynamic programming is not appropriate for such a large n, but other methods can be used to incorporate uncertainty. We will discuss two approaches that have been taken to deal with uncertainty in these nonlinear dynamic systems including a weighted feedback method (Whiffen and Shoemaker, Water Resources Research 1993) and sensitivity analysis of the nonlinear optimization (Minsker and Shoemaker, Water Resources Research, 1999).

Part II of the talk

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