Semidefinite characterization of sum-of-squares cones in algebras (Q2866191)

This is a refreshing survey of semidefinite representable cones of sum-of-squares elements in general abstract algebras, allowing to revisit previously known formulations relevant in optimization and systems control. It contains many references of historical relevance, and it can be used as an algebraic flavoured companion to other such overviews, the reviewer's favorites including \textit{M. Laurent} [in: Emerging applications of algebraic geometry. Papers of the IMA workshops Optimization and control, January 16--20, 2007 and Applications in biology, dynamics, and statistics, March 5--9, 2007, held at IMA, Minneapolis, MN, USA. Putinar, Mihai (ed.) et al., New York, NY: Springer. The IMA Volumes in Mathematics and its Applications 149, 157--270 (2009; Zbl 1163.13021)] and \textit{J. B. Lasserre} [Moments, positive polynomials and their applications. Imperial College Press Optimization Series 1. London: Imperial College Press (2010; Zbl 1211.90007)].