A Structured Quasi-Newton Algorithm for Optimizing with Incomplete Hessian Information
- Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Center for Applied Scientific Computing
- United Technologies Research Center, East Hartford, CT (United States)
- Argonne National Lab. (ANL), Lemont, IL (United States). Mathematics and Computer Science Div.
We present a structured quasi-Newton algorithm for unconstrained optimization problems that have unavailable second-order derivatives or Hessian terms. We provide a formal derivation of the well-known Broyden--Fletcher--Goldfarb--Shanno (BFGS) secant update formula that approximates only the missing Hessian terms, and we propose a linesearch quasi-Newton algorithm based on a modification of Wolfe conditions that converges to first-order optimality conditions. We also analyze the local convergence properties of the structured BFGS algorithm and show that it achieves superlinear convergence under the standard assumptions used by quasi-Newton methods using secant updates. In conclusion, we provide a thorough study of the practical performance of the algorithm on the CUTEr suite of test problems and show that our structured BFGS-based quasi-Newton algorithm outperforms the unstructured counterpart(s).
- Research Organization:
- Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)
- Sponsoring Organization:
- USDOE National Nuclear Security Administration (NNSA)
- Grant/Contract Number:
- AC52-07NA27344
- OSTI ID:
- 1574637
- Alternate ID(s):
- OSTI ID: 1573037
- Report Number(s):
- LLNL-JRNL--745068; 900344
- Journal Information:
- SIAM Journal on Optimization, Journal Name: SIAM Journal on Optimization Journal Issue: 2 Vol. 29; ISSN 1052-6234
- Publisher:
- SIAMCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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