Accelerating Sequential Quadratic Programming for Inequality-Constrained Optimization near Critical Lagrange Multipliers

Abstract

We consider a sequential quadratic programming algorithm for optimization problems with equality and inequality constraints, equipped with the standard Armijo linesearch procedure for a nonsmooth exact penalty function, intended for globalization of convergence. We are interested in the case when the standard assumptions for local superlinear convergence of the method may not hold. Specifically, we allow for violation of standard constraint qualifications and second-order sufficient optimality conditions, in which case attraction to so-called critical Lagrange multipliers is known to have a negative impact on convergence rate. In these circumstances, some known acceleration techniques can be expected to take effect only provided the true Hessian and the full SQP step are asymptotically accepted, and these are the main issues addressed in this work. The presented constructions extend some previously known ones to the case when inequality constraints are involved.