Applied Mathematics and Optimization
SIAM Journal on Optimization
On the Sequential Quadratically Constrained Quadratic Programming Methods
Mathematics of Operations Research
A Class of Active-Set Newton Methods for Mixed Complementarity Problems
SIAM Journal on Optimization
Journal of Computational and Applied Mathematics
A Truncated SQP Method Based on Inexact Interior-Point Solutions of Subproblems
SIAM Journal on Optimization
A working set SQCQP algorithm with simple nonmonotone penalty parameters
Journal of Computational and Applied Mathematics
Sharp Primal Superlinear Convergence Results for Some Newtonian Methods for Constrained Optimization
SIAM Journal on Optimization
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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 (SIAM J. Optim. 12, 949---978, 2002) 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 (SIAM J. Optim. 13, 1098---1119, 2003) under the assumption of convexity, the Slater constraint qualification, and a strong second-order sufficient condition. We obtain a new local convergence result, which 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 results apply 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.