On optimal zero-preserving corrections for inconsistent linear systems

Authors:
Paula Amaral;Luís M. Fernandes;Joaquim Júdice;Hanif D. Sherali
Affiliations:
Departamento de Matemática, Universidade Nova de Lisboa, Monte da Caparica, Portugal;Instituto Politécnico de Tomar and Instituto Telecomunicações, Coimbra, Portugal;Departamento de Matemática, Universidade de Coimbra and Instituto Telecomunicações, Coimbra, Portugal;Grado Department of Industrial & Systems Engineering, Virginia Polytechnic Institute & State University, Blacksburg, USA
Venue:
Journal of Global Optimization
Year:
2009

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Abstract

This paper addresses the problem of finding an optimal correction of an inconsistent linear system, where only the nonzero coefficients of the constraint matrix are allowed to be perturbed for reconstructing a consistent system. Using the Frobenius norm as a measure of the distance to feasibility, a nonconvex minimization problem is formulated, whose objective function is a sum of fractional functions. A branch-and-bound algorithm for solving this nonconvex program is proposed, based on suitably overestimating the denominator function for computing lower bounds. Computational experience is presented to demonstrate the efficacy of this approach.