Preprint A270/2004
Newton-type methods for optimization problems without constraint qualifications

Mikhail Solodov | Izmailov, Alexey

**Keywords: **
constraints degeneracy | regularity | Newton method | mathematical programs with complementarity constraints

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
constraints, we further extend our approach
to mixed equality and inequality-constrained
problems, and to mathematical programs with complementarity
constraints (MPCC). In particular, for MPCC we obtain a local
algorithm with quadratic convergence under the second-order
sufficient condition only, without any constraint qualifications,
not even the special MPCC constraint qualifications.