Many problems arising in data analysis can be formulated as a large sparse strictly convex quadratic programming problems with equality and inequality linear constraints. In order to solve these problems, we propose an iterative scheme based on a splitting of the matrix of the objective function and called splitting algorithm (SA). This algorithm transforms the original problem into a sequence of subproblems easier to solve, for which there exists a large number of efficient methods in literature. Each subproblem can be solved as a linear complementarity problem or as a constrained least distance problem. We give conditions for SA convergence and we present an application on a large scale sparse problem arising in constrained bivariate interpolation. In this application we use a special version of SA called diagonalization algorithm (DA). An extensive experimentation on CRAY C90 permits to evaluate the DA performance.
Splitting methods for quadratic optimization in data analysis / Galligani, Emanuele; V., Ruggiero; Zanni, Luca. - In: INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS. - ISSN 0020-7160. - STAMPA. - 63:(1997), pp. 289-307.