Extensions of Yuan’s Lemma to fourth-order tensor system with applications

  • Qingzhi Yang
  • Yuning Yang
  • Yang Zhou
    • Categories Constrained Nonlinear Optimization, Semi-definite Programming Short URL: https://optimization-online.org/?p=15033

    Yuan’s lemma is a basic proposition on homogeneous quadratic function system. In this paper, we extend Yuan’s lemma to 4th-order tensor system. We first give two gen- eralized definitions of positive semidefinite of 4th-order tensor, and based on them, two extensions of Yuan’s lemma are proposed. We illustrate the difference between our ex- tensions and existing another extension of Yuan’s lemma. We also put forward several 4th-order tensor optimization problems and show extended Yuan’s lemma how to be applied.

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    School of Mathematical Sciences and LPMC, Nankai University, 1/2018

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