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In this paper, we present several new rank-one decomposition theorems for Hermitian positive semidefinite matrices, which generalize our previous results The new matrix rank-one decomposition theorems appear to have wide applications in theory as well as in practice. On the theoretical side, for example, we show how to further extend some of the classical(More)
In this paper we present a polynomial-time procedure to find a low rank solution for a system of Linear Matrix Inequalities (LMI). The existence of such a low rank solution was shown in Au-Yeung and Poon [1] and Barvinok [3]. In Au-Yeung and Poon's approach, an earlier unpublished manuscript of Bohnenblust [6] played an essential role. Both proofs in [1](More)
In this paper we propose a new class of primal-dual path-following interior point algorithms for solving monotone linear complementarity problems. At each iteration, the method would select a target on the central path with a large update from the current iterate, and then the Newton method is used to get the search directions, followed by adaptively(More)
In this paper we consider the problem of minimizing a nonconvex quadratic function, subject to two quadratic inequality constraints. As an application, such quadratic program plays an important role in the trust region method for nonlinear optimization; such problem is known as the CDT subproblem in the literature. The Lagrangian dual of the CDT subproblem(More)
In this paper we propose a new class of primal-dual path-following interior point algorithms for solving monotone linear complementarity problems. At each iteration, the method would select a target on the central path with a large update from the current iterate, and then the Newton method is used to get the search directions, followed by adaptively(More)
We study the problem of multicast routing and wavelength assignment (MC-RWA) in multi-hop optical WDM networks with respect to several target functions. Specially, we first study the MC-RWA problem under the target of minimize maximum hops, an efficient MC-RWA algorithm was proposed for that case. But for the objective of minimizing the total number of(More)
In this paper we investigate the problem of cooperative beamforming design in cognitive radio network with a primary network and a secondary network. In the secondary network, the two transmitters communicate by the help of relays each other, and the relays select the amplify-and-forward (AF). The aim of this paper is to minimize the total power of relays(More)
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