A STRUCTURED QUASI-NEWTON ALGORITHM FOR OPTIMIZING WITH INCOMPLETE HESSIAN INFORMATION

doi:10.1137/18M1167942

Title: A STRUCTURED QUASI-NEWTON ALGORITHM FOR OPTIMIZING WITH INCOMPLETE HESSIAN INFORMATION

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Abstract

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. 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).

Authors:: Petra, Cosmin G.; Chiang, Nai-Yuan; Anitescu, Mihai

Publication Date:: 2019-01-01

Research Org.:: Argonne National Lab. (ANL), Argonne, IL (United States)

Sponsoring Org.:: USDOE Office of Science (SC); National Science Foundation (NSF)

OSTI Identifier:: 1573037

DOE Contract Number:: AC02-06CH11357

Resource Type:: Journal Article

Journal Name:: SIAM Journal on Optimization

Additional Journal Information:: Journal Volume: 29; Journal Issue: 2

Country of Publication:: United States

Language:: English

Citation Formats


                    Petra, Cosmin G., Chiang, Nai-Yuan, and Anitescu, Mihai. A STRUCTURED QUASI-NEWTON ALGORITHM FOR OPTIMIZING WITH INCOMPLETE HESSIAN INFORMATION.  United States: N. p., 2019. 
        Web.  doi:10.1137/18M1167942.

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                    Petra, Cosmin G., Chiang, Nai-Yuan, & Anitescu, Mihai. A STRUCTURED QUASI-NEWTON ALGORITHM FOR OPTIMIZING WITH INCOMPLETE HESSIAN INFORMATION.  United States.  doi:10.1137/18M1167942.

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                    Petra, Cosmin G., Chiang, Nai-Yuan, and Anitescu, Mihai. Tue .  
        "A STRUCTURED QUASI-NEWTON ALGORITHM FOR OPTIMIZING WITH INCOMPLETE HESSIAN INFORMATION".  United States.  doi:10.1137/18M1167942.

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@article{osti_1573037,

  title        = {A STRUCTURED QUASI-NEWTON ALGORITHM FOR OPTIMIZING WITH INCOMPLETE HESSIAN INFORMATION},

  author       = {Petra, Cosmin G. and Chiang, Nai-Yuan and Anitescu, Mihai},

  abstractNote = {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. 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).},

  doi          = {10.1137/18M1167942},

  journal      = {SIAM Journal on Optimization},
number       = 2,

  volume       = 29,

  place        = {United States},

  year         = {2019},

  month        = {1}

}

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DOI: 10.1137/18M1167942

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