Convergence of the Implicit Filtering Method for Constrained Optimization of Noisy Functions

REFERENCES

• E.J. Anderson and M.C. Ferris ( 2001 ). A direct search algorithm for optimization with noisy function evaluations . SIAM J. Optimiz. 11 : 837 – 857 .
   Google Scholar
• A. Battermann , J.M. Gablonsky , A. Patrick , C.T. Kelley , K.R. Kavanagh , T. Coffey , and C.T. Miller ( 2002 ). Solution of a groundwater control problem with implicit filtering . Optimiz. Eng. 3 : 189 – 199 .
   Google Scholar
• D.P. Bertsekas ( 1976 ). On the Goldstein-Levitin-Polyak gradient projection method . IEEE Trans. Autom. Control 21 : 174 – 184 .
   Web of Science ®Google Scholar
• J.V. Burke and J.J. Moré ( 1988 ). On the identification of active constraints . SIAM J. Numer. Anal. 25 : 1197 – 1211 .
   Web of Science ®Google Scholar
• P.H. Calamai and J.J. Moré ( 1987 ). Projected gradient methods for linearly constrained problems . Math. Programming 39 : 93 – 116 .
   Web of Science ®Google Scholar
• R.G. Carter , J.M. Gablonsky , A. Patrick , C.T. Kelley , and O.J. Eslinger ( 2001 ). Algorithms for noisy problems in gas transmission pipeline optimization . Optimiz. Eng. 2 : 139 – 157 .
   Google Scholar
• T.D. Choi and C.T. Kelley ( 2000 ). Superlinear convergence and implicit filtering . SIAM J. Optimiz. 10 : 1149 – 1162 .
   Web of Science ®Google Scholar
• T.D. Choi , O.J. Eslinger , C.T. Kelley , J.W. David , and M. Etheridge ( 2000 ). Optimization of automotive valve train components with implicit filtering . Optimiz. Eng. 1 : 9 – 27 .
   Google Scholar
• J.W. David , C.T. Kelley , and C.Y. Chen ( 1996 ). Use of an implicit filtering algorithm for mechanical system parameter identification. SAE Paper 960358, In Modeling of CI and SI Engines, 1996 SAE International Congress and Exposition Conference Proceedings , Society of Automotive Engineers , Washington , D.C. , pp. 189 – 194 .
   Google Scholar
• C. Elster and A. Neumaier ( 1995 ). A grid algorithm for bound-constrained optimization of noisy function . IMA J. Numer. Anal. 15 : 585 – 608 .
   Web of Science ®Google Scholar
• C. Elster and A. Neumaier ( 1997 ). A trust-region method for the optimization of noisy functions . Computing 58 : 31 – 46 .
   Google Scholar
• K.R. Fowler , C.T. Kelley , C.T. Miller , C.E. Kees , R.W. Darwin , J.P. Reese , M.W. Farthing , and M.S.C. Reed ( 2004 ). Solution of a well-field design problem with implicit filtering . Optimiz. Eng. 5 : 207 – 234 .
   Google Scholar
• E.M. Gafni and D.P. Bertsekas ( 1984 ). Two-metric projection methods for constrained optimization . SIAM J. Control Optimiz. 22 : 936 – 964 .
   Web of Science ®Google Scholar
• P. Gilmore and C.T. Kelley ( 1995 ). An implicit filtering algorithm for optimization of functions with many local minima . SIAM J. Optimiz. 5 : 269 – 285 .
   Web of Science ®Google Scholar
• T. Glad and A. Goldstein ( 1977 ). Optimization of functions whose values are subjected to small errors . BIT 17 : 160 – 169 .
   Google Scholar
• M. Hintermüller ( 2002 ). Solving nonlinear programming problems with noisy function values and noisy gradients . J. Optim. Theory Appl. 114 : 133 – 169 .
   Google Scholar
• C.T. Kelley ( 1999 ). Iterative Methods for Optimization . No. 18 in Frontiers in Applied Mathematics , SIAM , Philadelphia .
   Google Scholar
• B.T. Polyak (1987). Introduction to Optimization . Optimization Software Inc ., New York.
   Google Scholar
• D.E. Stoneking , G.L. Bilbro , R.J. Trew , P. Gilmore , and C.T. Kelley , ( 1992 ). Yield optimization using a GaAs process simulator coupled to a physical device model . IEEE Trans. Microwave Theory Techniques 40 : 1353 – 1363 .
   Google Scholar
• PH.L. Toint ( 1988 ). Global convergence of a class of trust region methods for nonconvex minimization in Hilbert space . IMA J. Numer. Anal. 8 : 231 – 252 .
   Web of Science ®Google Scholar
• V. Torczon ( 1997 ). On the convergence of pattern search algorithms . SIAM J. Optimiz. 7 : 1 – 25 .
   Web of Science ®Google Scholar
• T.A. Winslow , R.J. Trew , P. Gilmore , and C.T. Kelley ( 1991 ). Doping profiles for optimum class B performance GaAs MESFET amplifiers. In Proceedings IEEE/Cornell Conference on Advanced Concepts in High Speed Devices and Circuits, IEEE , Piscataway , NJ , pp. 188 – 197 .
   Google Scholar
• E.H. Zarantonello ( 1971 ). Projections on convex sets in Hilbert space and spectral theory . In: Contributions to Nonlinear Functional Analysis . ( E.H. Zarantonello , ed.) Academic Press , New York , pp. 237–424.
   Google Scholar