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Space tensor conic programming

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  • Liqun Qi
  • Yinyu Ye

Abstract

Space tensors appear in physics and mechanics. Mathematically, they are tensors in the three-dimensional Euclidean space. In the research area of diffusion magnetic resonance imaging, convex optimization problems are formed where higher order positive semi-definite space tensors are involved. In this short paper, we investigate these problems from the viewpoint of conic linear programming (CLP). We characterize the dual cone of the positive semi-definite space tensor cone, and study the CLP formulation and the duality of positive semi-definite space tensor conic programming. Copyright Springer Science+Business Media New York 2014

Suggested Citation

  • Liqun Qi & Yinyu Ye, 2014. "Space tensor conic programming," Computational Optimization and Applications, Springer, vol. 59(1), pages 307-319, October.
    • Handle: RePEc:spr:coopap:v:59:y:2014:i:1:p:307-319
    DOI: 10.1007/s10589-013-9577-0
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    References listed on IDEAS

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    1. NESTEROV, Yurii & TODD, Michael & YE, Yinyu, 1996. "Primal-Dual Methods and Infeasibility Detectors for Nonlinear Programming Problems," LIDAM Discussion Papers CORE 1996037, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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    Cited by:

    1. Shenglong Hu & Guoyin Li & Liqun Qi, 2016. "A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure," Journal of Optimization Theory and Applications, Springer, vol. 168(2), pages 446-474, February.

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