Newton-Type Methods for Optimization Problems without Constraint Qualifications

@article{Izmailov2004NewtonTypeMF,
  title={Newton-Type Methods for Optimization Problems without Constraint Qualifications},
  author={Alexey F. Izmailov and Mikhail V. Solodov},
  journal={SIAM Journal on Optimization},
  year={2004},
  volume={15},
  pages={210-228}
}
We consider equality-constrained optimization problems, where a given solution may not satisfy any constraint qualification but satisfies the standard second-order sufficient condition for optimality. Based on local identification of the rank of the constraints degeneracy via the singular-value decomposition, we derive a modified primal-dual optimality system whose solution is locally unique, nondegenerate, and thus can be found by standard Newton-type techniques. Using identification of active… CONTINUE READING
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