A Multidimensional Filter SQP Algorithm for Nonlinear Programming (Journal of Computational Mathematics, 2020)
We propose a multidimensional filter SQP algorithm. The multidimensional filter technique proposed by Gould et al. [SIAM J. Optim., 2005] is extended to solve constrainedoptimization problems. In our proposed algorithm, the constraints are partitioned intoseveral parts, and the entry of our filter consists of these different parts. Not only the criteria for accepting a trial step would be relaxed, but the individual behavior of each partof constraints is considered. One feature is that the undesirable link between the objective function and the constraint violation in the filter acceptance criteria disappears. Theother is that feasibility restoration phases are unnecessary because a consistent quadraticprogramming subproblem is used. We prove that our algorithm is globally convergent toKKT points under the constant positive generators (CPG) condition which is weaker thanthe well-known Mangasarian-Fromovitz constraint qualification (MFCQ) and the constantpositive linear dependence (CPLD). Numerical results are presented to show the efficiencyof the algorithm.