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Peter J.C. Dickinson (peter.dickinsoncantab.net) Abstract: In this paper we consider the set of polynomials which are nonnegative over a subset of the nonnegative orthant, where this subset is described by homogeneous polynomial inequalities. The study of such a set of polynomials is motivated by copositivity and the fact that any bounded polynomial optimisation problem can be reformulated into a conic optimisation problem over such a set. The main work of this paper is to introduce a new hierarchy of linear inner approximations for such a set. This hierarchy can then be improved through the use of positive semidefiniteness. Advantages to these approaches are discussed and some examples are presented. Keywords: real algebraic geometry; copositive optimization; approximation hierarchy; conic optimization; nonnegative polynomials; polynomial optimization Category 1: Linear, Cone and Semidefinite Programming Citation: Submitted Download: [PDF] Entry Submitted: 06/16/2013 Modify/Update this entry  
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