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Award Abstract # 0707220
Iterative Methods for Nonlinear Equations and Optimization

NSF Org: DMS
Division Of Mathematical Sciences
Recipient: NORTH CAROLINA STATE UNIVERSITY
Initial Amendment Date: July 27, 2007
Latest Amendment Date: July 27, 2007
Award Number: 0707220
Award Instrument: Standard Grant
Program Manager: Michael Steuerwalt
DMS  Division Of Mathematical Sciences
MPS  Directorate for Mathematical and Physical Sciences
Start Date: August 1, 2007
End Date: July 31, 2011 (Estimated)
Total Intended Award Amount: $263,084.00
Total Awarded Amount to Date: $263,084.00
Funds Obligated to Date: FY 2007 = $263,084.00
History of Investigator:
  • Carl Kelley (Principal Investigator)
     tim_kelley@ncsu.edu
Recipient Sponsored Research Office: North Carolina State University
 2601 WOLF VILLAGE WAY
 RALEIGH
 NC  US  27695-0001
(919)515-2444
Sponsor Congressional District: 02
Primary Place of Performance: North Carolina State University
 2601 WOLF VILLAGE WAY
 RALEIGH
 NC  US  27695-0001
Primary Place of Performance
Congressional District:		 02
Unique Entity Identifier (UEI): U3NVH931QJJ3
Parent UEI: U3NVH931QJJ3
NSF Program(s): APPLIED MATHEMATICS,
COMPUTATIONAL MATHEMATICS
Primary Program Source: app-0107 
Program Reference Code(s): 0000, 9263, OTHR
Program Element Code(s): 126600, 127100
Award Agency Code: 4900
Fund Agency Code: 4900
Assistance Listing Number(s): 47.049

ABSTRACT

Kelley
0707220

The principal investigator studies numerical methods for the
solution of nonlinear equations and optimization problems with a
focus on continuation methods, nonsmooth problems, and multilevel
methods for integral equations. The main topics of the research
are (1) the development and analysis of multilevel continuation
algorithms for optimization problems with integral equation
constraints and the application of those methods in simulating
atomic and molecular fluids, (2) the design and analysis of
continuation/quasi-Newton methods for nonsmooth nonlinear least
squares, with applications to calibration of models of blood
flow, (3) continued study of the conditioning of the linear
systems and eigenproblems that arise when pseudo-arclength
continuation is used in bifurcation analysis, and (4) multi-model
methods in which one physical model, based on differential or
integral equations, for example, is used as a preconditioner for
a solver which is based on a more accurate, more expensive to
evaluate model, such as a molecular dynamics or stochastic
simulation.

Nonlinear equations and optimization problems are commonly
encountered in science and engineering. Motivated by
applications in chemistry and medicine, the principal
investigator studies equations with multiple solutions, the
challenge being to determine which of those solutions represents
the real world and which cannot be seen in actual physical
systems, and optimization problems for which standard methods and
computer codes fail. This work should lead to new approaches
useful in many branches of science and engineering.

PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH

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(Showing: 1 - 10 of 13)
M. Gee, C. T. Kelley, and R. B. Lehoucq "Pseudo-Transient Continuation for Nonlinear Transient Elasticity" International Journal for Numerical Methods in Engineering , v.78 , 2009
M. Marucho, C. T. Kelley, and B. M. Pettitt "Solutions of the optimized closure integral equation theory: heteronuclear polyatomic fluids" J. Chem. Th. Comp , v.4 , 2008 , p.385
C. T. Kelley, L. Qi, L-Z. Liao, J. P. Reese, and C. Winton "Projected Pseudo-Transient Continuation" SIAM J. Numer. Anal , v.46 , 2008 , p.3071
David Mokrauer, C. T. Kelley, Alexei Bykhovski "Efficient Parallel Computation of Molecular Potential Surfaces for the Study of Light-Induced Transition Dynamics in Multiple Coordinates" IEEE Transactions on Nanotechnology , v.10 , 2011 , p.70
Dickson, KI; Kelley, CT; Ipsen, ICF; Kevrekidis, IG "Condition estimates for pseudo-arclength continuation" SIAM JOURNAL ON NUMERICAL ANALYSIS , v.45 , 2007 , p.263 View record at Web of Science 10.1137/06065438
G. W. Characklis, B. R. Kirsch, K. E. M. Dillard, C. T. Kelley "More Efficient Optimization of Long-Term Water Supply Portfolios" Water Resources Research , v.45 , 2009 , p.W03414-1 10.1029/2008WR007018
G. W. Characklis, B. R. Kirsch, K. E. M. Dillard, C. T. Kelley "More Efficient Optimization of Long-Term Water Supply Portfolios" Water Resources Research , v.45 , 2009 , p.W03414-1 10.1029/2008WR007018
I. C. F. Ipsen, C. T. Kelley, S. R. Pope "Nonlinear Least Squares Problems and Subset Selection" SIAM J. Numer. Anal , v.49 , 2011
K. R. Fowler, J. P. Reese, C. E. Kees, J. E. Dennis, C. T. Kelley, C. T. Miller, C. Audet, A. J. Booker, G. Couture, R. W. Darwin, M. W. Farthing, D. E. Finkel, J. M. Gablonsky, G. Gray, and T. G. Kolda "A Comparison of Derivative-Free Optimization Methods for Groundwater Supply and Hydraulic Capture Problems" Water Resources Research , v.31 , 2008 , p.743 "10.1016/j.advwatres.2008.10.010
L-H. Zhang, C. T. Kelley, and L.-Z. Liao "A continuous Newton-type method for unconstrained optimization" Pacific Journal on Optimization , v.4 , 2008 , p.259
M. Marucho, C. T. Kelley, and B. M. Pettitt "Solutions of the optimized closure integral equation theory: heteronuclear polyatomic fluids" J. Chem. Th. Comp , v.4 , 2008 , p.385
(Showing: 1 - 10 of 13)

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