Difference Of Convex Programming Problem Research Articles

Load Control Problems in Direct Current Distribution Networks: Optimality, Equilibrium of Games

Due to the promising development of direct current (dc) distribution networks, we focus on the demand-side management (DSM) problems which aim at the minimization of operational costs in dc distribution networks. Based on the established voltage model of power electronic loads, we formulate a DSM optimization problem that coordinates the bus voltage by minimizing the system cost, and the underlying optimization problem is nonconvex. In order to solve this nonconvex problem, we first reformulate it as a difference of convex programming problem, and then propose a novel algorithm based on branch and bound to implement the optimal solution. It is shown that the system is guaranteed to converge to the global optimum under the proposed method. As demonstrated with numerical examples, we analyze the convergence and global optimality of the proposed method, and discuss the computational complexity and scalability with respect to the size of distribution networks. Moreover, in case each of individual loads can make its own decisions by itself, the underlying optimization problem is implemented in the context of the noncooperative game. The existence of the Nash equilibrium is verified and demonstrated through simulation results.

Robust Power Optimization for Downlink Cloud Radio Access Networks with Physical Layer Security.

Since the cloud radio access network (C-RAN) transmits information signals by jointly transmission, the multiple copies of information signals might be eavesdropped on. Therefore, this paper studies the resource allocation algorithm for secure energy optimization in a downlink C-RAN, via jointly designing base station (BS) mode, beamforming and artificial noise (AN) given imperfect channel state information (CSI) of information receivers (IRs) and eavesdrop receivers (ERs). The considered resource allocation design problem is formulated as a nonlinear programming problem of power minimization under the quality of service (QoS) for each IR, the power constraint for each BS, and the physical layer security (PLS) constraints for each ER. To solve this non-trivial problem, we first adopt smooth -norm approximation and propose a general iterative difference of convex (IDC) algorithm with provable convergence for a difference of convex programming problem. Then, a three-stage algorithm is proposed to solve the original problem, which firstly apply the iterative difference of convex programming with semi-definite relaxation (SDR) technique to provide a roughly (approximately) sparse solution, and then improve the sparsity of the solutions using a deflation based post processing method. The effectiveness of the proposed algorithm is validated with extensive simulations for power minimization in secure downlink C-RANs.

Enhancing Performance of Random Caching in Large-Scale Wireless Networks With Multiple Receive Antennas

To improve signal-to-interference ratio (SIR) and make better use of file diversity provided by random caching, we consider two types of linear receivers, i.e., maximal ratio combining (MRC) receiver and partial zero forcing (PZF) receiver, at users in a large-scale cache-enabled single-input multi-output network. First, for each receiver, by utilizing tools from stochastic geometry, we derive a tractable expression and a tight upper bound for the successful transmission probability (STP). In the case of the MRC receiver, we also derive a closed-form expression for the asymptotic outage probability in the low SIR threshold regime. Then, for each receiver, we maximize the STP. In the case of the MRC receiver, we consider the maximization of the tight upper bound on the STP by optimizing the caching probabilities, which is a non-convex problem. We obtain a stationary point, by solving an equivalent difference of convex programming problem using concave-convex procedure. We also obtain a closed-form asymptotically optimal solution in the low SIR threshold regime. In the case of the PZF receiver, we consider the maximization of the tight upper bound on the STP by optimizing the caching probabilities and the degrees of freedom allocation (for boosting signal power and canceling interference), which is a mixed discrete-continuous problem. Based on structural properties, we obtain a low-complexity near optimal solution by using an alternating optimization approach. The analysis and optimization results reveal the impact of antenna resource at users on random caching.

Joint Beamformer Design for Wireless Fronthaul and Access Links in C-RANs

This paper presents a joint design framework of fronthaul and access links in cloud radio access networks, wherein the fronthaul data delivery between the central processor (CP) and small-cell base stations (SBSs) is carried over wireless links, which is more cost effective and flexible than the conventional wired fronthaul solutions. In this framework, the coordinated beamforming scheme is adopted by the SBSs to serve the users cooperatively, which not only reduces the bandwidth requirement over the fronthaul links, but also eliminates the inter-cell interference in the access links. To further exploit the spatial diversity over the fronthaul links, the multi-user beamforming scheme is adopted by the CP to deliver the data of all users to their serving SBSs simultaneously. This non-convex and combinatorial optimization problem is reformulated to a unified beamformer design problem using the $\ell _{0}/\ell _{1}$ -norm framework, which is still difficult to obtain the optimal solutions. Therefore, we first propose an algorithm based on the difference of convex (DC) programming scheme to find the suboptimal solutions, whereby the formulated problem is transformed to the standard DC programming problem and solved iteratively using the convex-concave procedure algorithm. We then propose another algorithm based on the successive convex approximation and weighted minimum-mean-squared-error approaches, and solve the transformed problem using the block coordinate update scheme. The pros and cons of these two algorithms are discussed, and simulation results are provided to demonstrate the performance gain of our schemes over other benchmark schemes.

Regularized LTI System Identification with Multiple Regularization Matrix

Regularization methods with regularization matrix in quadratic form have received increasing attention. For those methods, the design and tuning of the regularization matrix are two key issues that are closely related. For systems with complicated dynamics, it would be preferable that the designed regularization matrix can bring the hyper-parameter estimation problem certain structure such that a locally optimal solution can be found efficiently. An example of this idea is to use the so-called multiple kernel Chen et al. (2014) for kernel-based regularization methods. In this paper, we propose to use the multiple regularization matrix for the filter-based regularization. Interestingly, the marginal likelihood maximization with the multiple regularization matrix is also a difference of convex programming problem, and a locally optimal solution could be found with sequential convex optimization techniques.

Energy-Efficient Resource Allocation for mmWave Massive MIMO HetNets With Wireless Backhaul

In this paper, we investigate the energy-efficient resource allocation in two-tier massive multiple-input multiple-output (mMIMO) heterogeneous networks with wireless backhaul. Millimeter wave frequency is adopted at the mMIMO macro base station (MBS), and the cellular frequency is considered at small cell BS with orthogonal frequency-division multiple access. To lower the hardware cost and energy consumption at the MBS, two hybrid analog/digital precoding schemes are proposed according to the connectivity, i.e., fully connected and subarray structures. In order to design the small cell cluster-based power and subchannel allocation, we aim to maximize the energy efficiency of the system with limited wireless backhaul and users’ quality of service constraints. The formulated problem is non-convex mixed integer nonlinear fraction programming, which is non-trivial to solve directly. By exploiting fractional programming, we propose a two-loop iterative resource allocation algorithm to solve the nonconvex problem. Specifically, integer relaxation and a Dinkelback method are considered to transform the outer loop problem into a difference of convex programming (DCP). Following this, the first-order Taylor approximation is considered to linearize this inner loop DCP problem into a convex optimization framework. Lagrange dual problem is considered to obtain the closed-form power allocation. Furthermore, we prove the convergence of the proposed iterative algorithm. Numerical results are provided to validate our proposed schemes.

ADMM-Based Fast Algorithm for Multi-Group Multicast Beamforming in Large-Scale Wireless Systems

Multi-group multicast beamforming in wireless systems with large antenna arrays and massive audience is investigated in this paper. Multicast beamforming design is a well-known non-convex quadratically constrained quadratic programming (QCQP) problem. A conventional method to tackle this problem is to approximate it as a semi-definite programming problem via semi-definite relaxation, whose performance, however, deteriorates considerably as the number of per-group users goes large. A recent attempt is to apply convex-concave procedure (CCP) to find a stationary solution by treating it as a difference of convex programming problem, whose complexity, however, increases dramatically as the problem size increases. In this paper, we propose a low-complexity high-performance algorithm for multi-group multicast beamforming design in large-scale wireless systems by leveraging the alternating direction method of multipliers (ADMM) together with CCP. In specific, the original non-convex QCQP problem is first approximated as a sequence of convex subproblems via CCP. Each convex subproblem is then reformulated as a novel ADMM form. Our ADMM reformulation enables that each updating step is performed by solving multiple small-size subproblems with closed-form solutions in parallel. Numerical results show that our fast algorithm maintains the same favorable performance as state-of-the-art algorithms but reduces the complexity by orders of magnitude.

Human Activity Recognition in Smart Homes Based on a Difference of Convex Programming Problem

Human Activity Recognition in Smart Homes Based on a Difference of Convex Programming Problem

System Identification Via Sparse Multiple Kernel-Based Regularization Using Sequential Convex Optimization Techniques

Model estimation and structure detection with short data records are two issues that receive increasing interests in System Identification. In this paper, a multiple kernel-based regularization method is proposed to handle those issues. Multiple kernels are conic combinations of fixed kernels suitable for impulse response estimation, and equip the kernel-based regularization method with three features. First, multiple kernels can better capture complicated dynamics than single kernels. Second, the estimation of their weights by maximizing the marginal likelihood favors sparse optimal weights, which enables this method to tackle various structure detection problems, e.g., the sparse dynamic network identification and the segmentation of linear systems. Third, the marginal likelihood maximization problem is a difference of convex programming problem. It is thus possible to find a locally optimal solution efficiently by using a majorization minimization algorithm and an interior point method where the cost of a single interior-point iteration grows linearly in the number of fixed kernels. Monte Carlo simulations show that the locally optimal solutions lead to good performance for randomly generated starting points.

A sequential convex program method to DC program with joint chance constraints

In this paper, we consider a DC (difference of convex) programming problem with joint chance constraints (JCCDCP). Wepropose a DC function to approximate the constrained function and a corresponding DC program ($\textrm{P}_{\varepsilon}$) to approximate the JCCDCP.Under some mild assumptions, we show that the solution of Problem ($\textrm{P}_{\varepsilon}$) converges to the solution of JCCDCP when $\varepsilon\downarrow 0$. A sequential convex program method is constructed to solve the Problem ($\textrm{P}_{\varepsilon}$). At each iteration a convex program is solved based on the Monte Carlo method, and the generated optimal sequence is proved to convergeto the stationary point of Problem ($\textrm{P}_{\varepsilon}$).