Non-convex Constraints Research Articles

Fourier-spectral method for the Landau–Lifshitz–Gilbert equation in micromagnetism

The Landau–Lifshitz–Gilbert (LLG) equation models the temporal evolution of magnetization in continuum ferromagnets. The LLG equation has a nonconvex constraint and is highly nonlinear. In this paper, we will use the Fourier-spectral method for approximating the solution of the LLG equation with the nonconvex constraint. We consider the penalty problem and show the stability and convergence of the approximate penalty problem, and then we show the convergence of the penalty problem to a (weak) solution of the LLG equation. Computational experiments and comparison with other numerical methods are presented to demonstrate the effectiveness of the proposed method.

Optimized FACTS Devices for Power System Enhancement: Applications and Solving Methods

The use of FACTS devices in power systems has become increasingly popular in recent years, as they offer a number of benefits, including improved voltage profile, reduced power losses, and increased system reliability and safety. However, determining the optimal type, location, and size of FACTS devices can be a challenging optimization problem, as it involves mixed integer, nonlinear, and nonconvex constraints. To address this issue, researchers have applied various optimization techniques to determine the optimal configuration of FACTS devices in power systems. The paper provides an in-depth and comprehensive review of the various optimization techniques that have been used in published works in this field. The review classifies the optimization techniques into four main groups: classical optimization techniques, metaheuristic methods, analytic methods, and mixed or hybrid methods. Classical optimization techniques are conventional optimization approaches that are widely used in optimization problems. Metaheuristic methods are stochastic search algorithms that can be effective for nonconvex constraints. Analytic methods involve sensitivity analysis and gradient-based optimization techniques. Mixed or hybrid methods combine different optimization techniques to improve the solution quality. The paper also provides a performance comparison of these different optimization techniques, which can be useful in selecting an appropriate method for a specific problem. Finally, the paper offers some advice for future research in this field, such as developing new optimization techniques that can handle the complexity of the optimization problem and incorporating uncertainties into the optimization model. Overall, the paper provides a valuable resource for researchers and practitioners in the field of power systems optimization, as it summarizes the various optimization techniques that have been used to solve the FACTS optimization problem and provides insights into their performance and applicability.

$\mathcal{l}_{1}$ Filtering for Positive Takagi–Sugeno Fuzzy Systems via Successive Linear Programming

This paper studies the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {l}_{1}$</tex-math></inline-formula> filtering problem for positive Takagi-Sugeno (T-S) fuzzy systems. A pair of filters are sought to assure stability and positivity of filtering error systems with guaranteed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {l}_{1}$</tex-math></inline-formula> performance indices. For this purpose, a pair of linear co-positive Lyapunov functions that capture the positivity characteristics of filtering error systems are adopted to derive sufficient conditions for the existence of filters, which boils down to the bilinear programming problem. To solve this dilemma, we propose a convex approximation strategy, and thus a sequence of convex surrogates are developed to reasonably replace the non-convex constraints, based on which a successive linear programming algorithm is constructed. Therefore, the filters can be achieved by solving a battery of linear programmings. Finally, the efficiency of the designed filtering scheme was justified by simulation validations.

Energy Minimization for UAV Swarm-Enabled Wireless Inland Ship MEC Network With Time Windows

This paper establishes a new unmanned aerial vehicle (UAV) swarm-enabled wireless inland ship mobile edge computing (MEC) network with time windows, where UAVs are deployed to support time-constrained and low-resource unmanned surface vehicles (USVs) communication and computation. We aim to minimize UAV swarm energy consumption subject to numerous constraints. To tackle the challenging formulated problem, we decompose the original challenging problem into a list of sub-problems according to block coordinate descent (BCD) method and propose a heuristic algorithm to solve subproblems in an iterative manner. Specifically, the optimization of USVs offloading decisions is formulated as mixed-integer non-linear programming and then a modified deferred acceptance algorithm is proposed. The joint consideration of UAVs flight speed and UAV swarm stability is converted into a single-objective optimization problem after determining UAV control system’s latency requirements, and then Lagrangian multiplier method with Karush-Kuhn-Tucker (KKT) conditions is proposed. Successive convex approximations (SCA)-based algorithm is proposed to convert the non-convex constraints to convex ones, and then UAVs hovering coordinates can be obtained by solving the convex approximation problem. Numerical results verify the effectiveness of jointly considering USVs offloading decisions, UAVs flight speed, UAVs horizontal hovering coordinates and the number of UAVs for energy efficiency in comparison with several advanced baseline algorithms without optimization design.

A unified determinant-preserving formulation for compressible/incompressible finite viscoelasticity

This paper presents a formulation alongside a numerical solution algorithm to describe the mechanical response of bodies made of a large class of viscoelastic materials undergoing arbitrary quasistatic finite deformations. With the objective of having a unified formulation that applies to a wide range of highly compressible, nearly incompressible, and fully incompressible soft organic materials in a numerically tractable manner, the viscoelasticity is described within a Lagrangian setting by a two-potential mixed formulation. In this formulation, the deformation field, a pressure field that ensues from a Legendre transform, and an internal variable of state Fv that describes the viscous part of the deformation are the independent fields. Consistent with the experimental evidence that viscous deformation is a volume-preserving process, the internal variable Fv is required to satisfy the constraint detFv=1. To solve the resulting initial–boundary-value problem, a numerical solution algorithm is proposed that is based on a finite-element (FE) discretization of space and a finite-difference discretization of time. Specifically, a Variational Multiscale FE method is employed that allows for an arbitrary combination of shape functions for the deformation and pressure fields. To deal with the challenging non-convex constraint detFv=1, a new time integration scheme is introduced that allows to convert any explicit or implicit scheme of choice into a stable scheme that preserves the constraint detFv=1 identically. A series of test cases is presented that showcase the capabilities of the proposed formulation.

Research on Joint Beamforming of High-Speed Railway Millimeter-wave MIMO Communication with Reconfigurable Intelligent Surface

The advantage of a reconfigurable intelligent surface (RIS) is that it optimizes the wireless signal transmission environment. It can ameliorate the high loss of high-speed railway (HSR) millimeter-wave (mmWave) communications and increase signal strength by coherently superimposing signals at the receiving end through an appropriate beamforming design. In this paper, an mmWave multiple-input multiple-output communication system for HSR is discussed. The channel modeling takes into account the Doppler effect and the properties of mmWave channels. Aiming at the problem of high coupling of optimization variables, the singular value decomposition method is utilized to decouple them and to achieve the optimal active beamforming design. The original optimization problem is then rewritten into a more manageable form through a sequence of transformations. In order to overcome the restrictions imposed by non-convex constraints, the optimal RIS phase shift is directly calculated using the Riemann gradient descent (RGD) method. In this paper, spectral efficiency (SE) is taken as the optimization objective. Considering the fast time-varying environment of HSR, a step size selection scheme with easier convergence is adopted in the RGD method to complete the joint beamforming design. The numerical simulations demonstrate that the proposed solution outperforms the semi-definite relaxation scheme and the RIS-free auxiliary scheme in terms of SE performance and computational complexity.

Computationally Efficient Collision-Free Trajectory Planning of Satellite Swarms Under Unmodeled Orbital Perturbations

This paper studies the problem of collision-free trajectory planning for a satellite swarm reconfiguration under perturbations and modeling uncertainties in a low Earth orbit (LEO). Determining exact trajectory planning solutions is computationally heavy as they require solving a mixed-integer nonlinear program owing to i) nonlinear relative dynamic models of satellites, ii) fuel-optimal assignment of satellites on the final formation, and iii) nonconvex collision avoidance constraints. To address these, first, a suitable linear model for trajectory planning is identified by quantifying modeling accuracy associated with various models capturing LEO perturbations. The effects of any residual modeling errors in the path prediction are mitigated by shrinking-horizon model-predictive feedback control, which updates the control command based on the latest satellite measurements. Secondly, an optimal swarm configuration is efficiently computed by decoupling the target-assignment algorithm from the trajectory optimization problem. Based on the estimated fuel expenditure for each satellite–target pairing, the target-assignment algorithm selects a configuration with minimal fuel consumption. Lastly, to determine collision-free, fuel-optimal maneuvers, two novel trajectory planning approaches, namely, distributed and decentralized trajectory optimization, are presented. While the former iteratively searches for collision-free feasible paths to optimal terminal configuration, the latter computes a near-optimal configuration with collision-free paths.

Resource-Aware Video Delivery in Fog Radio Access Networks: A Joint QoE and QoS Perspective

In this paper, the video delivery strategy is studied under the cooperative framework of cache-enabled fog radio access networks (F-RAN), where multicast beamforming and video-quality selection are both taken into account in terms of different scenarios. In the user-centered scenario, an optimization problem regarding to the network quality of experience (QoE) improvement is first formulated under the essential quality of service (QoS) requirements of the users. Furthermore, an energy efficiency maximization scheme is proposed in the user-dense scenario to improve the resource utilization when network resources may be insufficient to guarantee the QoS requirements of all the users. In particular, a user scheduling scheme is studied in this case. More specifically, the non-convex constraints and fractional object functions in the aforementioned problems are dealt with by successive convex approximation (SCA) technique and the Dinkelbach approach. In order to solve the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{0}$</tex-math></inline-formula> -norm problem caused by user scheduling, we introduce the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$l_{1}$</tex-math></inline-formula> -norm approximation to improve the sparsity of the solution. Finally, the effectiveness of the proposed schemes is validated by extensive simulations.

A KKT Conditions Based Transceiver Optimization Framework for RIS-Aided Multiuser MIMO Networks

In many core problems of signal processing and wireless communications, Karush-Kuhn-Tucker (KKT) conditions based optimization plays a fundamental role. Hence we investigate the KKT conditions in the context of optimizing positive semidefinite matrix variables under nonconvex rank constraints. More explicitly, based on the properties of KKT conditions, we optimize a reconfigurable intelligent surface (RIS) aided multi-user multi-input multi-output (MU-MIMO) network. Specifically, we consider the capacity maximization and sum mean square error (MSE) minimization problems of both the RIS-aided MU-MIMO uplink (UL) and downlink (DL) under multiple weighted power constraints and rank constraints. As for the RIS-aided MU-MIMO UL, the optimal structures of the signal covariance matrices are derived based on the KKT conditions. Furthermore, an efficient procedure is designed for solving the capacity maximization and sum mean square error (MSE) minimization problems. Then the UL-DL dualities are exploited for solving the capacity maximization and MSE minimization problems of the RIS-aided MU-MIMO DL based on the results of the UL optimization. Hence in the proposed framework, the phase shifting matrix of the RIS is jointly optimized with the signal covariance matrices for both the UL and DL. Our simulation results demonstrate the performance advantages of the proposed framework.

Robust Beamforming for RIS Enhanced Transmissions in Cognitive Radio Networks

We propose a robust beamforming (BF) scheme for reconfigurable intelligent surface (RIS) enhanced transmission to support heterogeneous services with diverse signal-to-interference-plus-noise ratio requirements in cognitive radio networks (CRNs). Here, the CRN coexisting with a primary network offers connection-centric services and content-aware services through space division multiple access and RIS-aided multicast technology, respectively. Using imperfect statistical channel state information, the RIS enhanced transmission scheme is formulated as a non-convex optimization problem with outage constraints. To address this intractable problem, we first use the cumulative distribution function of a standard normal distribution and Schur complement approaches to transform the non-convex outage constraints into solvable ones. Then, a robust BF algorithm integrating alternate optimization with semidefinite relaxation methods is proposed to obtain the active BF weight vectors at the cognitive base station and the phase shift matrix at the RIS. Our simulation results demonstrate the robustness of the proposed BF algorithm and the superiority of the RIS enhanced wireless transmission.

Guaranteeing a Physically Realizable Battery Dispatch Without Charge-Discharge Complementarity Constraints

The non-convex complementarity constraints present a fundamental computational challenge in energy constrained optimization problems. In this work, we present a new, linear, and robust battery optimization formulation that sidesteps the need for battery complementarity constraints and integers and prove analytically that the formulation guarantees that all energy constraints are satisfied which ensures that the optimized battery dispatch is physically realizable. In addition, we bound the worst-case model mismatch and discuss conservativeness. Simulation results further illustrate the effectiveness of this approach.

Robust Sum-Rate Maximization in Transmissive RMS Transceiver-Enabled SWIPT Networks

In this article, we propose a state-of-the-art downlink communication transceiver design for transmissive reconfigurable metasurface (RMS)-enabled simultaneous wireless information and power transfer (SWIPT) networks. Specifically, a feed antenna is deployed in the transmissive RMS-based transceiver, which can be used to implement beamforming. According to the relationship between wavelength and propagation distance, the spatial propagation models of plane and spherical waves are built. Then, in the case of imperfect channel state information (CSI), we formulate a robust system sum-rate maximization problem that jointly optimizes RMS transmissive coefficient, transmit power allocation, and power splitting ratio design while taking account of the nonlinear energy harvesting model and outage probability criterion. Since the coupling of optimization variables, the whole optimization problem is nonconvex and cannot be solved directly. Therefore, the alternating optimization (AO) framework is implemented to decompose the nonconvex original problem. In detail, the whole problem is divided into three subproblems to solve. For the nonconvexity of the objective function, successive convex approximation (SCA) is used to transform it, and the penalty function method and difference-of-convex (DC) programming are applied to deal with the nonconvex constraints. Finally, we alternately solve the three subproblems until the entire optimization problem converges. Numerical results show that our proposed algorithm has convergence and better performance than other benchmark algorithms.

UAV Trajectory and Energy Efficiency Optimization in RIS-Assisted Multi-User Air-to-Ground Communications Networks

An air-to-ground downlink communication network consisting of a reconfigurable intelligent surface (RIS) and unmanned aerial vehicle (UAV) is proposed. In conjunction with a resource allocation strategy, the system’s energy efficiency is improved. Specifically, the UAV equipped with a RIS starts from an initial location, and an energy-efficient unmanned aerial vehicle deployment (EEUD) algorithm is deployed to jointly optimize the UAV trajectory, RIS phase shifts, and BS transmit power, so as to obtain a quasi-optimal deployment location and hence improve the energy efficiency. First, the RIS phase shifts are optimized by using the block coordinate descent (BCD) algorithm to deal with the nonconvex inequality constraint, and then integrated with the Dinkelbach algorithm to address the resource allocation problem of the BS transmit power. Finally, for solving the UAV trajectory optimization problem, the complex objective function is transformed into a convex function, and the optimal UAV flight trajectory is obtained. Our simulation results show that the quasi-optimal deployment location obtained by the EEUD algorithm is superior to other deployment strategies in energy efficiency. Moreover, the instantaneous energy efficiency of the UAVs along the trajectory of searching the deployment location is better than other comparison trajectories. Furthermore, the RIS-assisted multi-user air-to-ground communication network can offer up to 145% improvement in energy efficiency over the traditional amplify-and-forward (AF) relay.

An accurate RSS/AoA-based localization method for internet of underwater things

Localization is an important issue for Internet of Underwater Things (IoUT) since the performance of a large number of underwater applications highly relies on the position information of underwater sensors. In this paper, we propose a hybrid localization approach based on angle-of-arrival (AoA) and received signal strength (RSS) for IoUT. We consider a smart fishing scenario in which using the proposed approach fishers can find fishes’ locations effectively. The proposed method collects the RSS observation and estimates the AoA based on error variance. To have a more realistic deployment, we assume that the perfect noise information is not available. Thus, a minimax approach is provided in order to optimize the worst-case performance and enhance the estimation accuracy under the unknown parameters. Furthermore, we analyze the mismatch of the proposed estimator using mean-square error (MSE). We then develop semidefinite programming (SDP) based method which relaxes the non-convex constraints into the convex constraints to solve the localization problem in an efficient way. Finally, the Cramer–Rao lower bounds (CRLBs) are derived to bound the performance of the RSS-based estimator. In comparison with other localization schemes, the proposed method increases localization accuracy by more than 13%. Our method can localize 96% of sensor nodes with less than 5% positioning error when there exist 25% anchors.

A Post-Event Generator Start-Up Strategy for Renewable Penetrated Transmission System Considering Dynamic Frequency Regulation

Restoring transmission systems (TSs) with a high penetration of renewable generation is a troublesome task. To enhance the resilience of these TSs, a deterministic post-event generator start-up strategy (GSUS) is proposed in this paper, where the conventional and renewable units are co-operated. However, the utilization of renewable generation yields a concern that the recovering TS may be exposed to the risk of frequency instability since the renewable units have the characteristics of low inertia and high uncertainty. Consequently, dynamic frequency regulation (DFR) is considered while a novel approximate method is proposed to linearize the non-convex DFR constraints. Besides, a novel uncertainty set associated with restoring states is established to model the nodal power fluctuations. On the basic of the above works, a robust GSUS with DFR is developed. To solve this GSUS efficiently, an adaptive robust-based methodology is proposed to explore the “worst” realization of the uncertainty and then the non-convex bi-level robust constraints are reformulated. Finally, the effectiveness of our works is verified on a real-world 129-bus TS.

Asynchronous Activity Detection for Cell-Free Massive MIMO: From Centralized to Distributed Algorithms

Device activity detection in the emerging cell-free massive multiple-input multiple-output (MIMO) systems has been recognized as a crucial task in machine-type communications, in which multiple access points (APs) jointly identify the active devices from a large number of potential devices based on the received signals. Most of the existing works addressing this problem rely on the impractical assumption that different active devices transmit signals synchronously. However, in practice, synchronization cannot be guaranteed due to the low-cost oscillators, which brings additional discontinuous and nonconvex constraints to the detection problem. To address this challenge, this paper reveals an equivalent reformulation to the asynchronous activity detection problem, which facilitates the development of a centralized algorithm and a distributed algorithm that satisfy the highly nonconvex constraints in a gentle fashion as the iteration number increases, so that the sequence generated by the proposed algorithms can get around bad stationary points. To reduce the capacity requirements of the fronthauls, we further design a communication-efficient accelerated distributed algorithm. Simulation results demonstrate that the proposed centralized and distributed algorithms outperform state-of-the-art approaches, and the proposed accelerated distributed algorithm achieves close detection performance to that of the centralized algorithm but with a much smaller number of bits to be transmitted on the fronthaul links.

Distributed $${H_\infty }$$ Consensus Problem for First-Order Multi-Agent Systems with Antagonistic Interactions and Nonconvex Constraints

Distributed $${H_\infty }$$ Consensus Problem for First-Order Multi-Agent Systems with Antagonistic Interactions and Nonconvex Constraints

MIMO radar design with joint constant-modulus and any p-norm similarity constraints

MIMO radar plays a key role in many applications, e.g., autonomous driving, smart parking, and gesture recognition. The similarity waveform constraint is an important constraint for radar waveform design. However, the joint constant-modulus and similarity constraints pose a big challenge in MIMO radar design. Only the special case with ∞-norm similarity and constant-modulus constraints is tackled by the semidefinite relaxation (SDR) and the successive quadratic refinement (SQR) methods. In this paper, the joint constant-modulus and any p-norm (1≤p≤∞) similarity constraints are tackled by the proposed relax-and-retract algorithm. In particular, the nonconvex constant-modulus constraint is first relaxed to a convex constraint, and then the retract operation is guaranteed to recover a constant-modulus solution within a fixed iteration number. Extensive simulation results show that full range similarity control and constant-modulus constraints are satisfied under different p-norms. For the special case with 1-norm, it is firstly found to be a constant-modulus-inducing norm. For the special case with ∞-norm, the proposed relax-and-retract method has less computational complexity than the SDR and SQR approaches.

Flow shop scheduling with human–robot collaboration: a joint chance-constrained programming approach

ABSTRACT Human–robot collaboration has been incorporated into production and assembly processes to promote system flexibility, changeability and adaptability. However, it poses new challenges to resource allocation and production scheduling due to its intrinsic uncertainty and also the increasing complexity of resources. This paper investigates a stochastic flow shop scheduling problem in the context of human–robot collaboration. The goal is to achieve efficient utilisation of flexible resources including human workers and cobots and take full advantage of human–robot collaboration in production scheduling. A stochastic Cobb–Douglas production function is utilised to evaluate the production efficiency of human–robot collaboration considering instabilities of human performance. A joint chance-constrained programming model is formulated to ensure that the required system performance can be achieved. A CVaR approximation-based approach is proposed to solve the formulated model with mixed-integer variables and a nonconvex constraint. The effectiveness of the formulated model and the efficiency of the proposed solution approach are evaluated via numerical experiments. Computational results show the superiority of our solution approach over three other approaches including Bonferroni approximation, scenario approach and individual chance-constrained programming.

Distributed L2 − L∞ containment control with nonconvex constraints for multi-agent systems

This paper studies a distributed L2−L∞ containment control problem with or without considering nonconvex control input constraints. The main challenge is how to address nonconvex constraints while satisfying the L2−L∞ performance index function. A distributed algorithm is proposed using only the local information, and the containment control problem with nonconvex constraints and L2−L∞ performance can be solved. Based on the properties of the projection operator and convexity, the constrained L2−L∞ containment control problem can be solved under the undirected connected graphs. Finally, the effectiveness of the algorithm is verified by a numerical experiment.