Preprint A568/2007
STABILIZED SEQUENTIAL QUADRATIC PROGRAMMING FOR OPTIMIZATION AND A STABILIZED NEWTON-TYPE METHOD FOR VARIATIONAL PROBLEMS

Mikhail Solodov | Fernández, Damián

**Keywords: **
Stabilized sequential quadratic programming | Karush-Kuhn-Tucker system | variational inequality | Newton methods | superlinear convergence | error bound.

The stabilized version of the sequential quadratic programming algorithm
(sSQP) had been developed
in order to achieve fast convergence
despite possible degeneracy of constraints of optimization problems,
when the Lagrange multipliers associated to a solution are not unique.
Superlinear convergence of sSQP had been previously established
under the strong second-order sufficient condition for optimality
(without any constraint qualification assumptions).
We prove a stronger superlinear convergence result than the above,
assuming the usual second-order sufficient condition only.
In addition, our analysis is carried out
in the more general setting of
variational problems, for which we
introduce a natural extension of sSQP techniques.
In the process, we also obtain a new error bound for Karush-Kuhn-Tucker
systems for variational problems that holds under an
appropriate second-order condition.