  The cone of sums of nonnegative circuits (SONCs) is a subset of the cone of
nonnegative polynomials / exponential sums, which has been studied extensively
in recent years. In this article, we construct a subset of the SONC cone which
we call the DSONC cone. The DSONC cone can be seen as an extension of the dual
SONC cone; membership can be tested via linear programming. We show that the
DSONC cone is a proper, full-dimensional cone, we provide a description of its
extreme rays, and collect several properties that parallel those of the SONC
cone. Moreover, we show that functions in the DSONC cone cannot have real
zeros, which yields that DSONC cone does not intersect the boundary of the SONC
cone. Furthermore, we discuss the intersection of the DSONC cone with the SOS
and SDSOS cones. Finally, we show that circuit functions in the boundary of the
DSONC cone are determined by points of equilibria, which hence are the
analogues to singular points in the primal SONC cone, and relate the DSONC cone
to tropical geometry.
