Demir, Özlem Tuğfe
Tuncer, Temel Engin
Semidefinite relaxation (SDR) is a powerful approach to solve nonconvex optimization problems involving rank condition. However its performance becomes unacceptable for certain cases. In this paper, a nonconvex equivalent formulation without the rank condition is presented for the broadcast beamforming problem. This new formulation is exploited to obtain an alternating optimization method which is shown to converge to the local optimum rank one solution. Proposed method opens up new possibilities in different applications. Simulations show that the new method is very effective and can attain global optimum especially when the number of users is low.


Efficient preconditioning strategies for the multilevel fast multipole algorithm
Gurel, Levent; Malas, Tahir; Ergül, Özgür Salih (2007-03-30)
For the iterative solutions of the integral equation methods employing the multilevel fast multipole algorithm (MLFMA), effective preconditioning techniques should be developed for robustness and efficiency. Preconditioning techniques for such problems can be broadly classified as fixed preconditioners that are generated from the sparse near-field matrix and variable ones that can make use of MLFMA with the help of the flexible solvers. Among fixed preconditioners, we show that an incomplete LU precondition...
Ant Colony Search Method in Practical Structural Optimization
Hasançebi, Oğuzhan (2011-06-01)
This paper is concerned with application and evaluation of ant colony optimization (ACO) method to practical structural optimization problems. In particular, a size optimum design of pin-jointed truss structures is considered with ACO such that the members are chosen from ready sections for minimum weight design. The application of the algorithm is demonstrated using two design examples with practical design considerations. Both examples are formulated according to provisions of ASD-AISC (Allowable Stress D...
Iterative Rank Minimization For Broadcast Beamforming
Demir, Özlem Tuğfe; Tuncer, Temel Engin (2014-04-25)
Optimization problem of broadcast beamforming is nonconvex due to rank condition. Semidefinite relaxation (SDR) method is proposed to solve this problem. However, in certain cases, the performance of SDR becomes unacceptable. In this paper, an equivalent formulation of the original problem without rank condition is found. An iterative algorithm which is shown to converge to a rank one solution is presented. Experimental results show that the proposed algorithm is very effective and gives better results than...
Adaptive discontinuous Galerkin methods for convection dominated optimal control problems
Yücel, Hamdullah; Karasözen, Bülent; Department of Scientific Computing (2012)
Many real-life applications such as the shape optimization of technological devices, the identification of parameters in environmental processes and flow control problems lead to optimization problems governed by systems of convection di usion partial di erential equations (PDEs). When convection dominates di usion, the solutions of these PDEs typically exhibit layers on small regions where the solution has large gradients. Hence, it requires special numerical techniques, which take into account the structu...
Basis Reduction Methods
Patakı, Gabor; Tural, Mustafa Kemal (John Wiley and Sons, 2011-01-01)
We review lattice based methods to solve integer programming feasibility problems, in particular, the algorithms of Lenstra, and Kannan, and the reformulation methods of Aardal, et al. and of Krishnamoorthy and Pataki. The unifying theme in all of them is transforming the problem urn:x-wiley:9780470400531:media:eorms0093:xm1 where P is a polyhedron, into urn:x-wiley:9780470400531:media:eorms0093:xm2 where the columns of B are short, and near orthogonal, that is, they form a reduced basis of the generated l...
Citation Formats
Ö. T. Demir and T. E. Tuncer, “ALTERNATING MAXIMIZATION ALGORITHM FOR THE BROADCAST BEAMFORMING,” 2014, Accessed: 00, 2020. [Online]. Available: