A New Inexact Nonmonotone Filter Sequential Quadratic Programming Algorithm

Abstract

An inexact nonmonotone filter sequential quadratic programming algorithm is presented for solving general constrained nonlinear programming problems. At every iteration, a steering direction is computed as a minimizer of a linear model of the constraint violation over a trust region. A possible infeasible stationary point can be detected using the steering direction. If the current iterate is not an infeasible stationary point, a strongly convex feasible quadratic programming subproblem is defined to compute a search direction as an inexact solution satisfying some loose and achievable conditions. We prove that the search direction is a descent direction for the constraint violation or the objective function. Moreover, we use a penalty parameter updating strategy to yield the search direction as a descent direction for the penalty function. To attain a superlinear local convergence, an accelerating direction is computed in certain iterations. We use a nonmonotone filter strategy to compute the step-length along the accelerating direction or the search direction. The global convergence and superlinear local convergence of the algorithm can be obtained under some standard assumptions. Competitive numerical results obtained by an implementation of our algorithm are reported.