Shuzhong Zhang

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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)
Consider a communication system whereby multiple users share a common frequency band and must choose their transmit power spectral densities dynamically in response to physical channel conditions. Due to co-channel interference, the achievable data rate of each user depends on not only the power spectral density of its own, but also those of others in the(More)
We derive LMI-characterizations and dual decomposition algorithms for certain matrix cones which are generated by a given set using generalized co-positivity. These matrix cones are in fact cones of non-convex quadratic functions that are nonnegative on a certain domain. As a domain, we consider for instance the intersection of a (upper) level-set of a(More)
Metformin is among the most widely prescribed drugs for the treatment of type 2 diabetes. Organic cation transporter 1 (OCT1) plays a role in the hepatic uptake of metformin, but its role in the therapeutic effects of the drug, which involve activation of AMP-activated protein kinase (AMPK), is unknown. Recent studies have shown that human OCT1 is highly(More)
This paper establishes the superlinear convergence of a symmetric primal dual path following algorithm for semide nite programming under the assumptions that the semide nite pro gram has a strictly complementary primal dual optimal solution and that the size of the central path neighborhood tends to zero The interior point algorithm considered here closely(More)
In this paper we present several new results on minimizing an indefinite quadratic function under quadratic/linear constraints. The emphasis is placed on the case where the constraints are two quadratic inequalities. This formulation is termed the extended trust region subproblem in this paper, to distinguish it from the ordinary trust region subproblem(More)
Although the platinum-based anticancer drugs cisplatin, carboplatin, and oxaliplatin have similar DNA-binding properties, only oxaliplatin is active against colorectal tumors. The mechanisms for this tumor specificity of platinum-based compounds are poorly understood but could be related to differences in uptake. This study shows that the human organic(More)
We consider the NP-hard problem of finding a minimum norm vector in n-dimensional real or complex Euclidean space, subject to m concave homogeneous quadratic constraints. We show that a semidefinite programming (SDP) relaxation for this nonconvex quadratically constrained quadratic program (QP) provides an O(m) approximation in the real case, and an O(m)(More)
In this paper, we consider approximation algorithms for optimizing a generic multi-variate homogeneous polynomial function, subject to homogeneous quadratic constraints. Such optimization models have wide applications, e.g., in signal processing, magnetic resonance imaging (MRI), data training, approximation theory, and portfolio selection. Since polynomial(More)
This paper studies the possibilities of the Linear Matrix Inequality (LMI) characterization of the matrix cones formed by nonnegative complex Hermitian quadratic functions over specific domains in the complex space. In its real case analog, such studies were conducted in Sturm and Zhang [11]. In this paper it is shown that stronger results can be obtained(More)