This paper introduces a novel algorithmic solution for the approximation of a given multivariate function by a nomographic function that is composed of a one-dimensional continuous and monotone outer function and a sum of univariate continuous inner
functions. We show that a suitable approximation can be obtained by solving a cone-constrained Rayleigh-Quotient optimization problem. The proposed approach is based on a combination of a dimensionwise function decomposition known as Analysis of Variance (ANOVA) and optimization over a class of monotone polynomials. An example is given to show that the proposed algorithm can be applied to solve problems in distributed function computation over multiple-access channels.
This invited paper presents some novel ideas on how to enhance the performance of consensus algorithms in distributed wireless sensor networks, when communication costs are considered. Of particular interest are consensus algorithms that exploit the
broadcast property of the wireless channel to boost the performance in terms of convergence speeds. To this end, we propose a novel clustering based consensus algorithm that exploits interference for computation, while reducing the energy consumption in the network. The resulting optimization problem is a semidefinite program, which can be solved offline prior to system startup.
