Primal superlinear convergence results for some Newtonian methods

DAMIÁN FERNÁNDEZ; ALEXEY IZMAILOV; MIKHAIL SOLODOV

Bahía Blanca

Congreso; III congreso de Matemática Aplicada, Computacional e Industrial; 2011

ASAMACI

As is well known, Q-superlinear or Q-quadratic convergence of the primal-dual sequence generated by an optimization algorithm does not, in general, imply Q-superlinear convergence of the primal part. Primal convergence, however, is often of particular interest. For the sequential quadratic programming (SQP) algorithm, local primal-dual quadratic convergence can be established under the assumptions of uniqueness of the Lagrange multiplier associated to the solution and the second-order sufficient condition. At the same time, previous primal Q-superlinear convergence results for SQP required strengthening of the first assumption to the linear independence constraint qualification. We show that this strengthening of assumptions is actually not necessary. Our study is performed for a general perturbed SQP framework which covers, in addition to SQP and quasi-Newton SQP, the linearly constrained (augmented) Lagrangian (LCL) methods and the sequential quadratically constrained quadratic programming (SQCQP) methods.