In this work the numerical solution of linearly constrained quadratic programming problems is examined. This problem arises in many applications and it forms a basis for some algorithms that solve variational inequalities formulating equilibrium problems. An attractive iterative scheme for solving constrained quadratic programs when the matrix of the objective function is large and sparse consists in transforming, by a splitting of the objective matrix, the original problem into a sequence of subproblems easier to solve. At each iteration the subproblem is formulated as a linear complementarity problem that can be solved by methods suited for implementation on multiprocessor system. We analyse two parallel iterative solvers from the theoretical and practical point of view. Results of numerical experiments carried out on Cray T3D are reported.
Splitting methods and parallel solution of constrained quadratic programs / Galligani, Emanuele; V., Ruggiero; Zanni, Luca. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 0009-725X. - STAMPA. - Serie II, Supplemento al Volume 48:(1997), pp. 121-136. (Intervento presentato al convegno Equilibrium Problems with Side Constraints. Lagrangean Theory and Duality II tenutosi a Scilla (Reggio Calabria) nel 17-18 maggio 1996).