Anthony Man-Cho So

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In this article, we have provided general, comprehensive coverage of the SDR technique, from its practical deployments and scope of applicability to key theoretical results. We have also showcased several representative applications, namely MIMO detection, B¿ shimming in MRI, and sensor network localization. Another important application, namely downlink(More)
We analyze the semidefinite programming (SDP) based model and method for the position estimation problem in sensor network localization and other Euclidean distance geometry applications. We use SDP duality and interior-point algorithm theories to prove that the SDP localizes any network or graph that has unique sensor positions to fit given distance(More)
In this paper, we study a probabilistically robust transmit optimization problem under imperfect channel state information (CSI) at the transmitter and under the multiuser multiple-input single-output (MISO) downlink scenario. The main issue is to keep the probability of each user's achievable rate outage as caused by CSI uncertainties below a given(More)
Recently, robust transmit beamforming has drawn considerable attention because it can provide guaranteed receiver performance in the presence of channel state information (CSI) errors. Assuming complex Gaussian distributed CSI errors, this paper investigates the robust beamforming design problem that minimizes the transmission power subject to probabilistic(More)
Due to their fundamental nature and numerous applications, sphere constrained polynomial optimization problems have received a lot of attention lately. In this paper, we consider three such problems: (i) maximizing a homogeneous polynomial over the sphere; (ii) maximizing a multilinear form over a Cartesian product of spheres; and (iii) maximizing a(More)
In this paper we study semidefinite programming (SDP) models for a class of discrete and continuous quadratic optimization problems in the complex Hermitian form. These problems capture a class of well–known combinatorial optimization problems, as well as problems in control theory. For instance, they include the Max–3–Cut problem where the Laplacian matrix(More)
In physical-layer multicasting over a multiuser MISO downlink channel, transmit beamforming using semidefinite relaxation (SDR) has been a popular approach. In this paper, we propose a rank-2 transmit beamformed Alamouti space-time code scheme, which may be seen as a generalization of the previous SDR-based beamforming framework. The beamforming problem(More)
Kernel learning is a powerful framework for nonlinear data modeling. Using the kernel trick, a number of problems have been formulated as semidefinite programs (SDPs). These include Maximum Variance Unfolding (MVU) (Weinberger et al., 2004) in nonlinear dimensionality reduction, and Pairwise Constraint Propagation (PCP) (Li et al., 2008) in constrained(More)
In this paper, we consider various moment inequalities for sums of random matrices—which are well–studied in the functional analysis and probability theory literature—and demonstrate how they can be used to obtain the best known performance guarantees for several problems in optimization. First, we show that the validity of a recent conjecture of Nemirovski(More)
We propose a novel stochastic process that is with probability αi being absorbed at current state i, and with probability 1 − αi follows a random edge out of it. We analyze its properties and show its potential for exploring graph structures. We prove that under proper absorption rates, a random walk starting from a set S of low conductance will be mostly(More)