Splitting and projection-type methods for large convex quadratic programs (Q2718104)

This paper is strictly related to the earlier research by the authors on the splitting and projection-type methods for the solution of large linearly constrained quadratic programming (QP) problems. The aim of this work is to give a survey of the main results on the theoretical and numerical features of this last approach for large-scale QP problems, in particular, of the variable projection method (VPM) and the adaptive variable projection method (AVPM). It is admitted that the classical splitting and projection method can be considered as a unified iterative scheme.NEWLINENEWLINENEWLINEA convergence theorem, summarising the convergence results concerning the unified iterative scheme, is proved. Under very general hypotheses the convergence for two variants (VPM method and AVPM method) of an iterative scheme that uses a variable scalar parameter at each step is obtained. Furthermore, the solution of the inner subproblems of the projection-type methods are discussed. Finally, the results of an extensive experimentation on the numerical behaviour of the projection-type methods are reported.