On local convergence of sequential quadratically-constrained quadratic-programming type methods, with an extension to variational problems
Mikhail Solodov | Fernández, Damián
Quadratically constrained quadratic programming | Karush-Kuhn-Tucker system | variational inequality | quadratic convergence | Dennis-Mor\'e condition
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, in the optimization case, 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 assumptions, 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, our result applies to Karush-Kuhn-Tucker systems 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.