Splitting methods for quadratic optimization in data analysis

This work was supported by MURST Project on Computational Mathematics and by CINECA Project on Parallel Computing, Italy

Abstract

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

Keywords:

• Linearly constrained strictly convex quadratic program
• large scale problem
• splitting method
• diagonalization method
• bivariate interpolation
• vector computer

C.R.Categories:

• G.1.6

This work was supported by MURST Project on Computational Mathematics and by CINECA Project on Parallel Computing, Italy

This work was supported by MURST Project on Computational Mathematics and by CINECA Project on Parallel Computing, Italy

Notes

This work was supported by MURST Project on Computational Mathematics and by CINECA Project on Parallel Computing, Italy