On local convergence of Sequential Quadratically-Constrained Quadratic-Programming type methods

DAMIÁN FERNÁNDEZ; MIKHAIL SOLODOV

Santiago

Congreso; International Congress on the Applications of Mathematics; 2006

Centro de Modelamiento Matemático

We consider the class of quadratically-constrained quadratic programming methods in the framework extended from optimization to more general variational problems. Previously, in the optimization case, Anitescu (2002), showed superlinear convergence of the primal sequence under Mangasarian-Fromovitz constraint qualification and the quadratic growth condition. Quadratic convergence of the primal-dual sequence was established by Fukushima, Luo and Tseng (2003) under the convexity assumptions, the Slater constraint qualification, and a strong second-order sufficient condition. We obtain a new local convergence result, wich complements 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, our result applies to variational problems beyond the optimization case. Finally, we provide a necessary and sufficient condition for superlinear convergence of the primal sequence under a Dennis-Moré type condition.