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Testing Regularity on Linear Semidefinite Optimization Problems

  • Conference paper
Operational Research

Part of the book series: CIM Series in Mathematical Sciences ((CIMSMS,volume 4))

Abstract

This paper presents a study of regularity of Semidefinite Programming (SDP) problems. Current methods for SDP rely on assumptions of regularity such as constraint qualifications (CQ) and well-posedness. In the absence of regularity, the characterization of optimality may fail and the convergence of algorithms is not guaranteed. Therefore, it is important to have procedures that verify the regularity of a given problem before applying any (standard) SDP solver. We suggest a simple numerical procedure to test within a desired accuracy if a given SDP problem is regular in terms of the fulfilment of the Slater CQ. Our procedure is based on the recently proposed DIIS algorithm that determines the immobile index subspace for SDP. We use this algorithm in a framework of an interactive decision support system. Numerical results using SDP problems from the literature and instances from the SDPLIB suite are presented, and a comparative analysis with other results on regularity available in the literature is made.

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Acknowledgements

The author would like to thank the anonymous referee for the valuable comments that have helped to improve the paper. This work was supported by Portuguese funds through the CIDMA – Center for Research and Development in Mathematics and Applications (University of Aveiro), and the Portuguese Foundation for Science and Technology (“FCT – Fundação para a Ciência e a Tecnologia”), within project UID/MAT/04106/2013.

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Authors and Affiliations

  1. University of Aveiro, Campus Universitário de Santiago, Aveiro, Portugal

    Eloísa Macedo

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  1. Eloísa Macedo
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Correspondence to Eloísa Macedo .

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Editors and Affiliations

  1. Department of Mathematics and LIAAD-INESC TEC, Polytechnic Institute of Bragança; School of Technology and Management, Bragança, Portugal

    João Paulo Almeida

  2. Faculty of Engineering, CEGI - INESC TEC; University of Porto, Porto, Portugal

    José Fernando Oliveira

  3. Department of Mathematics and LIAAD-INESC TEC, University of Porto, Porto, Portugal

    Alberto Adrego Pinto

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Macedo, E. (2015). Testing Regularity on Linear Semidefinite Optimization Problems. In: Almeida, J., Oliveira, J., Pinto, A. (eds) Operational Research. CIM Series in Mathematical Sciences, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-20328-7_13

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