On local convergence of Sequential Quadratically Constrained Quadratic Programming type methods

DAMIÁN FERNÁNDEZ; MIKHAIL SOLODOV

Goiânia-GO

Workshop; VI Brazilian Workshop on Continuous Optimization; 2005

Universidade Federal de Goiás

We consider the class of quadratically constrained quadratic programming  methods in the framework extended from optimization to more general Karush-Kuhn-Tucker systems (which can be related, for example, to variational inequalities). Previously, Anitescu showed superlinear convergence of the primal sequence under the Mangasarian-Fromovitz constraint qualification and the quadratic growth condition. Quadratic convergence of the primal-dual sequence was established by Fukushima, Luo and Tseng under the convexity assumption, the Slater constraint qualification, and a strong second-order sufficient condition. We obtain a new local result, different from the above (it is neither stronger nor weaker): we prove primal-dual quadratic convergence under the linear independence constraint qualification, strict complementarity, and a second-order sufficiency condition. Additionally, we provide a necessary and sufficient condition for superlinear convergence of the primal sequence under a Dennis-Moré type condition.