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World Congress on Global Optimization

WCGO 2019: Optimization of Complex Systems: Theory, Models, Algorithms and Applications pp 145–154Cite as

On Conic Relaxations of Generalization of the Extended Trust Region Subproblem

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 991))

Abstract

The extended trust region subproblem (ETRS) of minimizing a quadratic objective over the unit ball with additional linear constraints has attracted a lot of attention in the last few years due to its theoretical significance and wide spectra of applications. Several sufficient conditions to guarantee the exactness of its semidefinite programming (SDP) relaxation or second order cone programming (SOCP) relaxation have been recently developed in the literature. In this paper, we consider a generalization of the extended trust region subproblem (GETRS), in which the unit ball constraint in ETRS is replaced by a general, possibly nonconvex, quadratic constraint. We demonstrate that the SDP relaxation can further be reformulated as an SOCP problem under a simultaneous diagonalization condition of the quadratic form. We then explore several sufficient conditions under which the SOCP relaxation of GETRS is exact under Slater condition.

Supported by Shanghai Sailing Program 18YF1401700, Natural Science Foundation of China (NSFC) 11801087 and Hong Kong Research Grants Council under Grants 14213716 and 14202017.

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Author information

Authors and Affiliations

  1. School of Data Science, Fudan University, Shanghai, China

    Rujun Jiang

  2. School of Data Science, City University of Hong Kong, Hong Kong, China

    Duan Li

Authors
  1. Rujun Jiang
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  2. Duan Li
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Corresponding author

Correspondence to Rujun Jiang .

Editor information

Editors and Affiliations

  1. Computer science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai An Le Thi

  2. Computer Science and Applications Department, LGIPM, University of Lorraine, Metz Cedex 03, France

    Hoai Minh Le

  3. Laboratory of Mathematics, National Institute for Applied Sciences (INSA)-Rouen Normadie, Saint-Étienne-du-Rouvray Cedex, France

    Tao Pham Dinh

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Jiang, R., Li, D. (2020). On Conic Relaxations of Generalization of the Extended Trust Region Subproblem. In: Le Thi, H., Le, H., Pham Dinh, T. (eds) Optimization of Complex Systems: Theory, Models, Algorithms and Applications. WCGO 2019. Advances in Intelligent Systems and Computing, vol 991. Springer, Cham. https://doi.org/10.1007/978-3-030-21803-4_15

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