Copositivity and Complete Positivity

  • Abraham Berman

    Technion - Israel Institute of Technology, Haifa, Israel
  • Immanuel M. Bomze

    Universität Wien, Austria
  • Mirjam Dür

    Universität Augsburg, Germany
  • Naomi Shaked-Monderer

    The Max Stern Yezreel Valley College, Yezreel Valley, Israel
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A real matrix AA is called copositive if xTAx0x^TAx \ge 0 holds for all xR+nx \in \mathbb R^n_+. A matrix AA is called completely positive if it can be factorized as A=BBTA = BB^T , where BB is an entrywise nonnegative matrix. The concept of copositivity can be traced back to Theodore Motzkin in 1952, and that of complete positivity to Marshal Hall Jr. in 1958. The two classes are related, and both have received considerable attention in the linear algebra community and in the last two decades also in the mathematical optimization community. These matrix classes have important applications in various fields, in which they arise naturally, including mathematical modeling, optimization, dynamical systems and statistics. More applications constantly arise.

The workshop brought together people working in various disciplines related to copositivity and complete positivity, in order to discuss these concepts from different viewpoints and to join forces to better understand these difficult but fascinating classes of matrices.

Cite this article

Abraham Berman, Immanuel M. Bomze, Mirjam Dür, Naomi Shaked-Monderer, Copositivity and Complete Positivity. Oberwolfach Rep. 14 (2017), no. 4, pp. 3071–3120

DOI 10.4171/OWR/2017/52