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From abstract: "Our method is the first variant of Newton’s method that has both cheap iterations and provably fast global convergence". It seems interesting.

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"Cheap iterations" led me to expect a 1st order method, not requiring computing the matrix of 2nd derivatives, which is the bottleneck in large systems. But this does indeed rely on the Hessian, so I'm not sure what makes the iterations "cheap".

If you don't want to compute the Hessian, you're at the wrong address with Newton's method. Quasi-Newton methods is where you want to look.

Sure, or Nesterov's accelerated gradient descent or something. I'm just not sure what the authors mean by "cheap iterations".

Update: your other comment clarified this for me. It's cheap relative to other methods that work with non-self-concordant objectives.

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