This article focuses on optimization of polynomials in noncommuting variables, while taking into account sparsity the input data. A converging hierarchy semidefinite relaxations for eigenvalue and trace is provided. a noncommutative analogue results due to Lasserre [SIAM J. Optim. 17(3) (2006), pp. 822--843] Waki et al. 17(1) 218--242]. The Gelfand-Naimark-Segal (GNS) construction applied extra...

We propose new mathematical optimization models for generating sparse dynamical graphs, or networks, that can achieve synchronization. The synchronization phenomenon is studied using the Kuramoto model, defined in terms of adjacency matrix graph and coupling strength network, modelling so-called coupled oscillators. Besides sparsity, we aim to obtain graphs which have good connectivity properti...

In this paper, we focus on Stochastic Composite Optimization (SCO) for sparse learning that aims to learn a sparse solution. Although many SCO algorithms have been developed for sparse learning with an optimal convergence rate O(1/T ), they often fail to deliver sparse solutions at the end either because of the limited sparsity regularization during stochastic optimization or due to the limitat...

Abstract: This paper proposes a novel scheme for multi-static passive radar processing, based on soft-input soft-output processing and Bayesian sparse estimation. In this scheme, each receiver estimates the probability of target presence based on its received signal and the prior information received from a central processor. The resulting posterior target probabilities are transmitted to the c...