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Keywords:

  • Block relaxation;
  • Newton's method;
  • MM algorithm;
  • penalization;
  • augmented Lagrangian;
  • acceleration

Summary

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.