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DTSTAMP:20190719T085743Z
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DTSTART;TZID=Europe/Stockholm:20190612T111500
DTEND;TZID=Europe/Stockholm:20190612T114500
UID:submissions.pasc-conference.org_PASC19_sess107_pap_jan106@linklings.co
 m
SUMMARY:Preconditioning Nonlinear Conjugate Gradient with Diagonalized Qua
 si-Newton
DESCRIPTION:Paper\nComputer Science and Applied Mathematics\n\nPreconditio
 ning Nonlinear Conjugate Gradient with Diagonalized Quasi-Newton\n\nDener,
  Denchfield, Munson, Wild\n\nNonlinear conjugate gradient (NCG) methods ca
 n generate search directions using only first-order information and a few 
 dot products, making them attractive algorithms for solving large-scale op
 timization problems. However, even the most modern NCG methods can require
  large numbers of iterations and, therefore, many function evaluations to 
 converge to a solution. This poses a challenge for simulation-constrained 
 problems where the function evaluation entails expensive partial or ordina
 ry differential equation solutions. Preconditioning can accelerate converg
 ence and help compute a solution in fewer function evaluations. However, g
 eneral-purpose preconditioners for nonlinear problems are challenging to c
 onstruct. In this paper, we review a selection of classical and modern NCG
  methods, introduce their preconditioned variants, and propose a precondit
 ioner based on the diagonalization of the BFGS formula. As with the NCG me
 thods, this preconditioner utilizes only first-order information and requi
 res only a small number of dot products. Our numerical experiments using C
 UTEst problems indicate that the proposed preconditioner successfully redu
 ces the number of function evaluations at negligible additional cost for i
 ts update and application.<br /><br />Full paper: https://doi.org/10.1145/
 3324989.3325712
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