Stabilized sequential quadratic programming with an extension to variational problems

DAMIÁN FERNÁNDEZ; MIKHAIL SOLODOV

Campinas-SP

Workshop; VII Brazilian Workshop on Continuous Optimization; 2008

Universidade Estadual de Campinas / IMECC

The stabilized version of the sequential quadratic programming algorithm (sSQP) had been developed in order to achieve fast convergence despite possible degeneracy of constraints of optimization problems, when the Lagrange multipliers associated to a solution are not unique. Superlinear convergence of sSQP had been previously established under the second-order sufficient condition for optimality (SOSC) and the Mangasarian-Fromovitz constraint qualification, or under the strong second-order sufficient condition for optimality (in that case, without constraint qualification assumptions). We prove a stronger superlinear convergence result than the above, assuming SOSC only. In addition, our analysis is carried out in the more general setting of variational problems, for which we introduce a natural extension of sSQP techniques. In the process, we also obtain a new error bound for Karush-Kuhn-Tucker systems for variational problems.