On preconditioned and relaxed AVMM methods for quadratic programming problems with equality constraints

To iteratively compute a solution of the equality-constraint quadratic programming problem, by successively introducing relaxation parameters and skillfully adopting a preconditioning matrix, we establish a preconditioned and relaxed alternating variable minimization with multiplier (PRAVMM) method, which is a further generalization of the preconditioned alternating variable minimization with multiplier (PAVMM) method proposed by Bai and Tao (2016) (BIT Numer. Math. 56 (2016), 399-422). Based on rigorous matrix analysis we demonstrate the asymptotic convergence property of the PRAVMM method. Numerical results show that the PRAVMM method is feasible and effective for solving the equality-constraint quadratic programming problems.