An overview on projection-type methods for convex large-scale quadratic programs (Q2773698)

A well-known approach for solving large and sparse linearly constrained quadratic programming (QP) problems is given by the splitting and projection methods. After a survey on these classical methods, it is shown that they can be unified in a general iterative scheme consisting in solving a sequence of QP subproblems with the constraints of the original problem and an easily solvable Hessian matrix. A convergence theorem is given for this general scheme. In order to improve the numerical performance of these methods, they introduce two variants of a projection-type scheme that use a variable projection parameter at each step. The two variable projection methods differ in the strategy used to assure a sufficient decrease of the objective function at each iteration. They prove, under very general hypotheses, the convergence of these schemes and propose two practical, nonexpensive and efficient updating rules.NEWLINENEWLINEFor the entire collection see [Zbl 0992.49001].