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.

Splitting methods for quadratic optimization in data analysis

GALLIGANI, Emanuele;ZANNI, Luca
1997

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.
1997
63
289
307
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.
Galligani, Emanuele; V., Ruggiero; Zanni, Luca
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/613243
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