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The Hessian-vector product has been utilized to find a second-order stationary solution with strong complexity guarantee (e.g., almost linear time complexity in the problem's dimensionality).
Problem Complexity and Method Efficiency in Optimization
A. S. Nemirovsky and D. B. Yudin · 1983
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Trust Region Methods
A.R. Conn, N.I.M. Gould, and P.L. Toint · 2000
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Cubic regularization of newton method and its global performance
Yurii Nesterov and Boris T Polyak · 2006
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Gradient methods for minimizing composite objective function
Yurii Nesterov · 2007
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Complexity bounds for second-order optimality in unconstrained optimization
C. Cartis, N. I. M. Gould, and Ph. L. Toint · 2012
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Most tensor problems are np-hard
Christopher J. Hillar and Lek-Heng Lim · 2013
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