Abstract
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.
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