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A Brief Survey of Modern Optimization for Statisticians

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  • Kenneth Lange
  • Eric C. Chi
  • Hua Zhou

Abstract

type="main" xml:id="insr12022-abs-0001"> Modern computational statistics is turning more and more to high-dimensional optimization to handle the deluge of big data. Once a model is formulated, its parameters can be estimated by optimization. Because model parsimony is important, models routinely include non-differentiable penalty terms such as the lasso. This sober reality complicates minimization and maximization. Our broad survey stresses a few important principles in algorithm design. Rather than view these principles in isolation, it is more productive to mix and match them. A few well-chosen examples illustrate this point. Algorithm derivation is also emphasized, and theory is downplayed, particularly the abstractions of the convex calculus. Thus, our survey should be useful and accessible to a broad audience.

Suggested Citation

  • Kenneth Lange & Eric C. Chi & Hua Zhou, 2014. "A Brief Survey of Modern Optimization for Statisticians," International Statistical Review, International Statistical Institute, vol. 82(1), pages 46-70, April.
    • Handle: RePEc:bla:istatr:v:82:y:2014:i:1:p:46-70
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    File URL: http://hdl.handle.net/10.1111/insr.12022
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    References listed on IDEAS

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    Cited by:

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    3. Yoshihiro Kanno, 2018. "Robust truss topology optimization via semidefinite programming with complementarity constraints: a difference-of-convex programming approach," Computational Optimization and Applications, Springer, vol. 71(2), pages 403-433, November.

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