Search Results (7)

This paper addresses the NP-hard problem of solving the rank of a matrix in Robust Principal Component Analysis (RPCA) by proposing a nonconvex fractional regularization approximation. Compared to existing convex regularization (which often yields suboptimal solutions) and nonconvex regularization (which typically requires parameter selection), the proposed model effectively avoids parameter selection while preserving scale invariance. By introducing an auxiliary variable, we transform the problem into a nonconvex optimization problem with a separable structure. We use a more flexible Symmetric Alternating Direction Method of Multipliers (SADMM) to arrive at a solution and provide a rigorous convergence proof. In numerical experiments involving synthetic data, image recovery, and foreground–background separation for surveillance video, the proposed fractional regularization model demonstrates high computational accuracy, and its performance is comparable to that of many state-of-the-art algorithms. Full article

The Alternating Direction Method of Multipliers (ADMM) has proven to be an efficient approach for implementing linear programming (LP) decoding of low-density parity-check (LDPC) codes. By introducing penalty terms into the LP decoding model’s objective function, ADMM-based variable node penalized decoding effectively mitigates non-integral solutions, thereby improving frame error rate (FER) performance, especially in the low signal-to-noise ratio (SNR) region. In this paper, we leverage the ADMM framework to derive explicit iterative steps for solving the LP decoding problem for LDPC codes with penalty functions. To further enhance decoding efficiency and accuracy, We propose an LDPC code decoding algorithm based on the symmetric ADMM (S-ADMM). We also establish some contraction properties satisfied by the iterative sequence of the algorithm. Through simulation experiments, we evaluate the proposed S-ADMM decoder using three standard LDPC codes and three representative fifth-generation (5G) codes. The results show that the S-ADMM decoder consistently outperforms conventional ADMM penalized decoders, offering significant improvements in decoding performance. Full article

To solve the problem of aperture fill time (AFT) for wideband sparse arrays, variable fractional delay (VFD) FIR filters are applied to eliminate linear coupling between spatial and time domains. However, the large dimensions of the filter coefficient matrix result in high system complexity. To alleviate the computational burden of solving VFD filter coefficients, a novel multi–regultion minimax (MRMM) model utilizing the sparse representation technique has been presented. The error function is constrained by the introduction of L2–norm and L1–norm regularizations within the minimax criterion. The L2–norm effectively resolves the problems of overfitting and non–unique solutions that arise in the sparse optimization of traditional minimax (MM) models. Meanwhile, the use of multiple L1–norms enables the optimal design of the smallest sub–filter number and order of the VFD filter. To solve the established nonconvex model, an improved sequential–alternating direction method of multipliers (S–ADMM) algorithm for filter coefficients is proposed, which utilizes sequential alternation to iteratively update multiple soft–thresholding problems. The experimental results show that the optimized VFD filter reduces system complexity significantly and corrects AFT effectively in a wideband sparse array. Full article

As a promising paradigm, the Industrial Internet of Things (IIoT) provides a wide range of intelligent services through the interconnection and interaction of heterogeneous networks. The quality of these services depends on how the bandwidth is shared among different flows. Hence, it is critical to design a flexible flow control strategy in multi-region management scenarios. In this paper, we establish a flow optimization model based on the IIoT networks managed by multiple Software-Defined Networking (SDN) controllers. Specifically, it jointly optimizes the real-time delivery, route selection, and constrained resource allocation to maximize the total utilities of domains. Since the topology and resources within each domain are kept secret, the problem model belongs to a multi-block problem with coupling constraints, which is difficult to be solved directly. To this end, we first decompose the problem into several intra-domain subproblems, which can be solved in parallel. By considering the inter-domain communication problem, we then introduce the slack variables to implement the interaction among domains. Finally, we design a distributed Proximal Symmetric Alternating Direction Method of Multipliers (Prox-SADMM) algorithm to solve the above joint optimization problem. Through numerical simulations, we investigate the impact of data timeliness, multi-path routing, and resource constraints on the rate utility. The performance analysis confirms that the Prox-SADMM algorithm can be well applied to large-scale networks and provides guidance to set appropriate parameter values according to the realistic requirements of IIoT networks. Full article

Millimeter wave (mmWave) relying upon the multiple output multiple input (MIMO) is a new potential candidate for fulfilling the huge emerging bandwidth requirements. Due to the short wavelength and the complicated hardware architecture of mmWave MIMO systems, the conventional estimation strategies based on the individual exploitation of sparsity or low rank properties are no longer efficient and hence more modern and advance estimation strategies are required to recapture the targeted channel matrix. Therefore, in this paper, we proposed a novel channel estimation strategy based on the symmetrical version of alternating direction methods of multipliers (S-ADMM), which exploits the sparsity and low rank property of channel altogether in a symmetrical manner. In S-ADMM, at each iteration, the Lagrange multipliers are updated twice which results symmetrical handling of all of the available variables in optimization problem. To validate the proposed algorithm, numerous computer simulations have been carried out which straightforwardly depicts that the S-ADMM performed well in terms of convergence as compared to other benchmark algorithms and also able to provide global optimal solutions for the strictly convex mmWave joint channel estimation optimization problem. Full article

In order to build an active distribution system with multi virtual power plants (VPP), a decentralized two-stage stochastic dispatching model based on synchronous alternating direction multiplier method (SADMM) was proposed in this paper. Through the integration of distributed energy and large-scale electric vehicles (EV) in the distribution network by VPP group, coordinative complementarity, and global optimization were realized. On the premise of energy autonomy management of active distribution network (AND) and VPP, after ensuring the privacy of stakeholders, the power of tie-line was taken as decoupling variable based on SADMM. Furthermore, without the participation of central coordinators, the optimization models of VPPs and distribution networks were decoupled to achieve fully decentralized optimization. Aiming at minimizing their own operating costs, the VPPs aggregate distributed energy and large-scale EVs within their jurisdiction to interact with the upper distribution network. On the premise of keeping operation safe, the upper distribution network formulated the energy interaction plan with each VPP, and then, the global energy optimization management of the entire distribution system and the decentralized autonomy of each VPP were achieved. In order to improve the stochastic uncertainty of distributed renewable energy output, a two-stage stochastic optimization method including pre-scheduling stage and rescheduling stage was adopted. The pre-scheduling stage was used to arrange charging and discharging plans of EV agents and output plans of micro gas turbines. The rescheduling stage was used to adjust the spare resources of micro gas turbines to deal with the uncertainty of distributed wind and light. An example of active distribution system with multi-VPPs was constructed by using the improved IEEE 33-bus system, then the validity of the model was verified. Full article

This paper proposes a distributed robust dispatch approach to solve the economic dispatch problem of the interconnected systems with a high proportion of wind power penetration. First of all, the basic principle of synchronous alternating direction method of multipliers (SADMM) is introduced to solve the economic dispatch problem of the two interconnected regions. Next, the polyhedron set of the robust optimization method is utilized to describe the wind power output. To adjust the conservativeness of the polyhedron set, an adjustment factor of robust conservativeness is introduced. Subsequently, considering the operation characteristics of the DC tie line between the interconnected regions, an economic dispatch model with a high proportion of wind power penetration is established and parallel iteration based on SADMM is used to solve the model. In each iteration, the optimized power of DC tie lines is exchanged between the regions without requiring the participation of the superior dispatch center. Finally, the validity of the proposed model is verified by the examples of the 2-area 6-node interconnected system and the interconnection of several modified New England 39-node systems. The results show that the proposed model can meet the needs of the independent dispatch of regional power grids, effectively deal with the uncertainty of wind power output, and maximize the wind power consumption under the condition of ensuring the safe operation of the interconnected systems. Full article