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Title |
Multigrid Algorithms for Discretized Optimization Problems
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Speaker
E-mail
From |
Stephen Nash
snash@gmu.edu
George Mason University
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Date
Time
Location |
Thursday, September 20, 2001
10-11am (PST)
Bldg. 940, Auditorium (IMTL) (Sandia - CA)
Bldg. 980, Room 24 (Sandia - NM)
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Abstract |
Many large optimization problems represent a family of models of varying
size, corresponding to different discretizations. An example is the
optimization of systems governed by differential equations. In such
problems, one has a set of design variables along with a set of state
variables, the two sets of variables being related through a set of
differential equation constraints. The overall computational cost of
optimization is determined by the level of discretization used to
numerically solve the governing differential equations. If a fine
discretization is used, one expects a greater degree of physical and
mathematical fidelity to the problem under consideration, but the large
number of state variables can make the cost of optimization
prohibitive.
We present a multigrid algorithm that uses solutions to optimization
problems based on coarser discretizations, which are less expensive to
compute, in a systematic manner to obtain the solution of the
optimization problem based on a finer discretization. Of interest is
the fact that the approach is applicable in situations where multigrid
applied only to the solution of the differential equation might not be
effective. We give evidence (both theoretical and numerical) that a
multigrid approach can often be successful in the more general setting
of optimization, and that the optimization setting offers a number of
practical advantages for solving problems of this type.
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About the Speaker |
Stephen Nash is a Professor of Systems Engineering & Operations
Research, and is currently serving as Associate
Dean of the School of Information Technology and Engineering
at George Mason University.
Prior to joining the faculty at George Mason University,
he taught at The Johns Hopkins University.
His research activities are centered in scientific computing, especially
nonlinear programming, along with related
interests in statistical computing and optimal control.
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