Adaptive cubic overestimation methods for unconstrained optimization

  title={Adaptive cubic overestimation methods for unconstrained optimization},
  author={Coralia Cartis and Nicholas I. M. Gould and Philippe L. Toint}
An Adaptive Cubic Overestimation (ACO) algorithm for unconstrained optimization, generalizing a method due to Nesterov & Polyak (Math. Programming 108, 2006, pp 177-205), is proposed. At each iteration of Nesterov & Polyak’s approach, the global minimizer of a local cubic overestimator of the objective function is determined, and this ensures a significant improvement in the objective so long as the Hessian of the objective is Lipschitz continuous and its Lipschitz constant is available. The… CONTINUE READING
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