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Space tensor conic programming

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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.

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Acknowledgements

We thank two referees for their helpful comments.

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Authors and Affiliations

  1. Department of Applied Mathematics, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China

    Liqun Qi & Yinyu Ye

  2. Department of Management Science and Engineering, by courtesy, Electrical Engineering, Stanford University, Stanford, CA, 94305, USA

    Yinyu Ye

Authors
  1. Liqun Qi
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  2. Yinyu Ye
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Correspondence to Liqun Qi.

Additional information

Dedicated to our good friend Masao Fukushima on the occasion of his 65th birthday.

This work was partly supported by the Research Grant Council of Hong Kong (Grant No. PolyU 501909, 502510, 502111 and 501212).

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Qi, L., Ye, Y. Space tensor conic programming. Comput Optim Appl 59, 307–319 (2014). https://doi.org/10.1007/s10589-013-9577-0

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