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trustOptim: An R Package for Trust Region Optimization with Sparse Hessians

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  • Braun, Michael

Abstract

Trust region algorithms are nonlinear optimization tools that tend to be stable and reliable when the objective function is non-concave, ill-conditioned, or exhibits regions that are nearly flat. Additionally, most freely-available optimization routines do not exploit the sparsity of the Hessian when such sparsity exists, as in log posterior densities of Bayesian hierarchical models. The trustOptim package for the R programming language addresses both of these issues. It is intended to be robust, scalable and efficient for a large class of nonlinear optimization problems that are often encountered in statistics, such as finding posterior modes. The user must supply the objective function, gradient and Hessian. However, when used in conjunction with the sparseHessianFD package, the user does not need to supply the exact sparse Hessian, as long as the sparsity structure is known in advance. For models with a large number of parameters, but for which most of the cross-partial derivatives are zero (i.e., the Hessian is sparse), trustOptim offers dramatic performance improvements over existing options, in terms of computational time and memory footprint.

Suggested Citation

  • Braun, Michael, 2014. "trustOptim: An R Package for Trust Region Optimization with Sparse Hessians," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i04).
  • Handle: RePEc:jss:jstsof:v:060:i04
    DOI: http://hdl.handle.net/10.18637/jss.v060.i04
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    References listed on IDEAS

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    1. Bates, Douglas & Eddelbuettel, Dirk, 2013. "Fast and Elegant Numerical Linear Algebra Using the RcppEigen Package," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 52(i05).
    2. Nash, John C. & Varadhan, Ravi, 2011. "Unifying Optimization Algorithms to Aid Software System Users: optimx for R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i09).
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    Cited by:

    1. Marra, Giampiero & Wyszynski, Karol, 2016. "Semi-parametric copula sample selection models for count responses," Computational Statistics & Data Analysis, Elsevier, vol. 104(C), pages 110-129.
    2. Michael Braun & Paul Damien, 2016. "Scalable Rejection Sampling for Bayesian Hierarchical Models," Marketing Science, INFORMS, vol. 35(3), pages 427-444, May.
    3. Varadhan, Ravi, 2014. "Numerical Optimization in R: Beyond optim," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 60(i01).
    4. Alex Stringer & Patrick Brown & Jamie Stafford, 2021. "Approximate Bayesian inference for case‐crossover models," Biometrics, The International Biometric Society, vol. 77(3), pages 785-795, September.

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