This paper introduces robust optimization models for minimization of the network congestion ratio that can handle the fluctuation in traffic demands between nodes. The simplest and widely used model to minimize the congestion ratio, called the pipe model, is based on precisely specified traffic demands. However, in practice, network operators are often unable to estimate exact traffic demands as they can fluctuate due to unpredictable factors. To overcome this weakness, we apply robust optimization to the problem of minimizing the network congestion ratio. First, we review existing models as robust counterparts of certain uncertainty sets. Then we consider robust optimization assuming ellipsoidal uncertainty sets, and derive a tractable optimization problem in the form of second-order cone programming (SOCP). Furthermore, we take uncertainty sets to be the intersection of ellipsoid and polyhedral sets, and considering the mirror subproblems inherent in the models, obtain tractable optimization problems, again in SOCP form. Compared to the previous model that assumes an error interval on each coordinate, our models have the advantage of being able to cope with the total amount of errors by setting a parameter that determines the volume of the ellipsoid. We perform numerical experiments to compare our SOCP models with the existing models which are formulated as linear programming problems. The results demonstrate the relevance of our models in terms of congestion ratio and computation time.

Aiming at solving the performance degradation caused by the covariance matrix mismatch in wideband beamforming for conformal arrays, a novel adaptive beamforming algorithm is proposed in this paper. In this algorithm, the interference-plus-noise covariance matrix is firstly reconstructed to solve the desired signal contamination problem. Then, a sparse reconstruction method is utilized to reduce the high computational cost and the requirement of sampling data. A novel cost function is formulated by the focusing matrix and singular value decomposition. Finally, the optimization problem is efficiently solved in a second-order cone programming framework. Simulation results using a cylindrical array demonstrate the effectiveness and robustness of the proposed algorithm and prove that this algorithm can achieve superior performance over the existing wideband beamforming methods for conformal arrays.

Considering the obvious bias of the traditional interpolation method, a novel time delay estimation (TDE) interpolation method with sub-sample accuracy is presented in this paper. The proposed method uses a generalized extended approximation method to obtain the objection function. Then the optimized interpolation curve is generated by Second-order Cone programming (SOCP). Finally the optimal TDE can be obtained by interpolation curve. The delay estimate of proposed method is not forced to lie on discrete samples and the sample points need not to be on the interpolation curve. In the condition of the acceptable computation complexity, computer simulation results clearly indicate that the proposed method is less biased and outperforms the other interpolation algorithms in terms of estimation accuracy.

This paper considers coordinated linear precoding for rate optimization in downlink multicell, multiuser orthogonal frequency-division multiple access networks. We focus on two different design criteria. In the first, the weighted sum-rate is maximized under transmit power constraints per base station. In the second, we minimize the total transmit power satisfying the signal-to-interference-plus-noise-ratio constraints of the subcarriers per cell. Both problems are solved using standard conic optimization packages. A less complex, fast, and provably convergent algorithm that maximizes the weighted sum-rate with per-cell transmit power constraints is formulated. We approximate the non-convex weighted sum-rate maximization (WSRM) problem with a solvable convex form by means of a sequential parametric convex approximation approach. The second-order cone formulations of an objective function and the constraints of the optimization problem are derived through a proper change of variables, first-order linear approximation, and hyperbolic constraints transformation. This algorithm converges to the suboptimal solution while taking fewer iterations in comparison to other known iterative WSRM algorithms. Numerical results are presented to demonstrate the effectiveness and superiority of the proposed algorithm.

The wideband noise controlling performance of the delayless subband adaptive filtering technique is affected by the group delay and in-band aliasing distortion of analysis filter banks. A method of recursive second-order cone programming is proposed to design the uniform DFT modulated analysis filter banks, with a small in-band aliasing error and low group delay. Simulation results show that the noise controlling performance is improved with small residual noise power spectra, a high noise attenuation level and fast convergence rate.

A wideband beamformer with mainlobe control is proposed. To make the beamformer robust against pointing errors, inequality rather than equality constraints are used to restrict the mainlobe response, thus more degrees of freedom are saved. The constraints involved are nonconvex, therefore are linearly approximated so that the beamformer can be obtained by iterating a second-order cone program. Moreover, the response variance element is introduced to achieve a frequency invariant beamwidth. The effectiveness of the technique is demonstrated by numerical examples.

The core of the support vector machine (SVM) problem is a quadratic programming problem with a linear constraint and bounded variables. This problem can be transformed into the second order cone programming (SOCP) problems. An interior-point-method (IPM) can be designed for the SOCP problems in terms of storage requirements as well as computational complexity if the kernel matrix has low-rank. If the kernel matrix is not a low-rank matrix, it can be approximated by a low-rank positive semi-definite matrix, which in turn will be fed into the optimizer. In this paper we present two SOCP formulations for each SVM classification and regression problem. There are several search direction methods for implementing SOCPs. Our main goal is to find a better search direction for implementing the SOCP formulations of the SVM problems. Two popular search direction methods: HKM and AHO are tested analytically for the SVM problems, and efficiently implemented. The computational costs of each iteration of the HKM and AHO search direction methods are shown to be the same for the SVM problems. Thus, the training time depends on the number of IPM iterations. Our experimental results show that the HKM method converges faster than the AHO method. We also compare our results with the method proposed in Fine and Scheinberg (2001) that also exploits the low-rank of the kernel matrix, the state-of-the-art SVM optimization softwares SVMTorch and SVMlight. The proposed methods are also compared with Joachims 'Linear SVM' method on linear kernel.