Evaluation Complexity for Nonlinear Constrained Optimization Using Unscaled KKT Conditions and High-Order Models

@article{Birgin2016EvaluationCF,
  title={Evaluation Complexity for Nonlinear Constrained Optimization Using Unscaled KKT Conditions and High-Order Models},
  author={Ernesto G. Birgin and J. L. Gardenghi and Jos{\'e} Mario Mart{\'i}nez and Sandra A. Santos and Philippe L. Toint},
  journal={SIAM Journal on Optimization},
  year={2016},
  volume={26},
  pages={951-967}
}
The evaluation complexity of general nonlinear, possibly nonconvex, constrained optimization is analyzed. It is shown that, under suitable smoothness conditions, an $\epsilon$-approximate first-order critical point of the problem can be computed in order $O(\epsilon^{1-2(p+1)/p})$ evaluations of the problem's functions and their first $p$ derivatives. This is achieved by using a two-phase algorithm inspired by Cartis, Gould, and Toint [SIAM J. Optim., 21 (2011), pp. 1721--1739; SIAM J. Optim… CONTINUE READING

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