Convex Optimization Algorithm Research Articles

Distributed Task Management in Fog Computing: A Socially Concave Bandit Game

Fog computing leverages the task offloading capabilities at the network’s edge to improve efficiency and enable swift responses to application demands. However, the design of task allocation strategies in a fog computing network is still challenging because of the heterogeneity of fog nodes and uncertainties in system dynamics. We formulate the distributed task allocation problem as a social-concave game with bandit feedback and show that the game has a unique Nash equilibrium, which is implementable using no-regret learning strategies (regret with sublinear growth). We then develop two no-regret online decision-making strategies. One strategy, namely bandit gradient ascent with momentum, is an online convex optimization algorithm with bandit feedback. The other strategy, Lipschitz bandit with initialization, is an EXP3 multi-armed bandit algorithm. We establish regret bounds for both strategies and analyze their convergence characteristics. Moreover, we compare the proposed strategies with an allocation strategy named learning with linear rewards. Theoretical-and numerical analysis shows the superior performance of the proposed strategies for efficient task allocation compared to the state-of-the-art methods.

Quantized Control for Local Synchronization of Fractional-Order Neural Networks with Actuator Saturation

This brief discusses the use of quantized control with actuator saturation to achieve the local synchronization of master–slave fractional-order neural networks (FONNs). A refined sector condition (RSC) is proposed that addresses the issue of the simultaneous quantizer effects and actuator constraints. The RSC is used in the theoretical analysis of local synchronization in drive-response systems. The analysis employs inequality techniques on the Mittag–Leffler function and fractional-order Lyapunov theory. Additionally, this paper presents two convex optimization algorithms that aim to minimize the actuator’s costs and expand the admissible initial area (AIA). Finally, this paper employs a three-neuron FONN to demonstrate the efficacy of the proposed methods.

A 2D-DOA Sparse Estimation Method with Total Variation Regularization for Spatially Extended Sources

In this paper, a novel two-dimensional direction of arrival (2D-DOA) estimation method with total variation regularization is proposed to deal with the problem of sparse DOA estimation for spatially extended sources. In a general sparse framework, the sparse 2D-DOA estimation problem is formulated with the regularization of extended source characteristics including spatial position grouping, acoustic signal block sparse, and correlation features. An extended sources acoustic model, two-dimensional array manifold and its complete representation, total variation regularization penalty term, and the regularization equation are built, and are utilized to seek the solutions where the non-zero coefficients are grouped together with optimum sparseness. A total variation sparse 2D-DOA estimation model is constructed by combining total variation regularization with LASSO. The model can be easily solved by the convex optimization algorithm, and the solving process can promote the sparsity of the solution on the spatial derivatives and the solution itself. The theoretical analysis results show that the steps of decorrelation processing and angle matching of traditional 2D-DOA estimation methods could be avoided when adopting the proposed method. The proposed method has better robustness to noise, better sparsity, and faster estimation speed with higher resolution than traditional methods. It is promising to provide a coherent sources sparse representation of a non-strictly sparse field.

The algorithm research of low-rank matrix spectral reconstruction for ground targets

Recently, micro-spectrometer based on filter array has received extensive attention in terms of cost and size. Yet, the spectrometer will produce large noise in the work, which has a great impact on the spectral reconstruction. In this paper, a low-dimensional filter array is selected based on the K-means-PSO（Particle Swarm Optimization） method to achieve the purpose of data dimensionality reduction, which further reduces the cost and processing difficulty of the micro-spectrometer. To address the redundancy and poor accuracy of spectral reconstruction data obtained by micro-spectrometers, a convex optimization algorithm constrained by three-segment regularization of a low-rank-matrix (IReg-Cvx algorithm) was proposed for spectral reconstruction in this study. In order to test algorithm universality and stability better, we selected 120 kinds of ground spectral curves, and the low-dimensional filter array is fused with the IReg-Cvx algorithm. Apply the corresponding constraints according to the different slopes of the curve, and the high-quality spectral reconstruction of the ground object target spectrum can be stably realized under the noise environment of 30, 25, and 20 dB.

Joint Unmanned Aerial Vehicle Location and Beamforming and Caching Optimization for Cache-Enabled Multi-Unmanned-Aerial-Vehicle Networks

Due to the advantages such as high flexibility, low cost and easy implementation offered by unmanned aerial vehicles (UAVs), a UAV-assisted network is regard as an appealing solution to a seamless coverage, high disaster-tolerant and on-demand wireless system. In this paper, we focus on the downlink transmission in a cache-enabled UAV-assisted wireless communication network, where UAVs cache popular content from a macro base station in advance and cooperatively transfer the content to users. We aim to minimize the average transmission latency of the system and to formulate an optimization problem that jointly optimizes the UAV location, beamforming and caching strategy. However, the formulated problem is very challenging because of its non-convexity and the highly coupled optimization variables. To solve this resulting problem efficiently, we decompose it into two subproblems, namely UAV location and beamforming optimization, and UAV caching strategy optimization. The first subproblem is an NP-hard joint optimization problem, while the second one is a linear programing problem. By adopting the first-order Taylor expansion, we propose a convex optimization algorithm based on the difference-of-convex (DC) method. Specifically, we bring out a method to apply linear approximation in the DC-based algorithm, which is particularly suitable to the problems involving complicated summations. The numerical results demonstrate that the proposed DC-based iterative optimization algorithm can efficiently reduce the average transmission latency of the system.

Edge Collaborative Compressed Sensing in Wireless Sensor Networks for Mechanical Vibration Monitoring

This paper proposes a novel edge collaborative compressed sensing for mechanical vibration monitoring (MVM) to address the severe shortage of storage and computational resources and long delay in transmitting massive vibration data in wireless sensor networks (WSN) for MVM. It first combines compressed sensing (CS) and edge computing (EC) into a WSN to effectively solve the above problems. Based on the self-developed acquisition node (AN) and edge computing node (ECN), the proposed approach is implemented in the AN and ECN respectively. This enhances the acquisition efficiency and computing capacity of the WSN. Meanwhile, the sparse pattern of a mechanical fault signal is analyzed. In addition, the adaptive parameter adjustment mechanism (APA) for the alternating direction of multiplier method based on Anderson acceleration is proposed to generate a convex optimization algorithm with fast convergence to realize data reconstruction in the ECN. The results of comprehensive experiments demonstrate that the proposed method can reduce the transmission data by 70%, while maintaining high-precision bearing fault feature detection, compared with the Shannon sampling theory. Furthermore, the acquisition and transmission efficiencies are improved significantly. This provides a potential solution for practical engineering applications.

Doubly autoparallel structure and curvature integrals

On a statistical manifold, we can define autoparallel submanifolds and path integrals of the second fundamental forms (curvature integrals) for its primal and dual affine connections, respectively. A submanifold is called doubly autoparallel if it is simultaneously autoparallel with respect to the both connections. In this paper we first discuss common properties of such submanifolds. In particular we next give an algebraic characterization of them in Jordan algebras and show their applications. Further, we exhibit that both curvature integrals induced from dually flat structure are interestingly related to an unexpected quantity, i.e., iteration-complexity of the interior-point algorithms for convex optimization defined on a submanifold that is not doubly autoparallel.

Reconciling business analytics with graphically initialized subspace clustering for optimal nonlinear pricing

The relationship between price and quantity in nonlinear pricing transcends simple proportionality, as conditional rebates and discounts may be contingent upon the quantity of goods or services purchased by consumers. This dynamic introduces significant challenges for both consumers and business operators because incomplete information arises from the inherent uncertainty of consumer behavior. In light of this, the present research elucidates the pursuit of optimal nonlinear pricing strategies by business operators through an innovative data-driven approach. Our contributions encompass two distinctive facets: a novel unsupervised spectral clustering method, termed graphically initialized subspace clustering, and a decision optimization framework. The proposed data-driven method introduces an optimization problem aimed at minimizing subspace partitioning costs, leveraging the efficient utilization of a mixture multivariate skewed t distribution to effectively capture heavy users and to characterize their parametric behavioral patterns. In addition, the decision optimization component builds upon the aforementioned method, employing a convex optimization algorithm to enable seamless modification of attributes in nonlinear pricing, while ensuring revenue consistency during pre- and post-modification. Notably, we substantiate the interpretability and practical applicability of our proposed methodology in the realm of business analytics, through empirical analysis utilizing real-world data obtained from a cellular carrier. The findings of this study confirm the efficacy and viability of our approach in enabling business operators to navigate the complexities of nonlinear pricing optimization with confidence and informed decision-making.

Adaptive nonlinear group delay mode estimation

The decomposition of non-stationary signals remains a challenge in a wide variety of fields. Especially, the impulse or cross-mode signals are difficult to be reconstructed by recent methods due to their transient characteristic. Moreover, most methods rely heavily on the user-defined settings of the regularized parameter for the convex optimization algorithm. In this work, an adaptive nonlinear group delay mode estimation (ANGDME) algorithm is proposed by exploiting the sparsity of signals formulated as the nonlinear group delay model. The ANGDME introduces a complex Bayesian compressive sensing (CBCS) framework to process the sparse reconstruction. Then, a hierarchical Laplace scale mixture (LSM) prior is utilized to model dependencies among coefficients and provides superior probabilistic predictions. Furthermore, the estimator of amplitudes and group delays (GDs) of signals are obtained from the posterior distribution by Bayesian inference instead of point estimation. Finally, the proposed method updates the dictionary matrix in a traditional data-driven manner, resulting in a high-resolution time-frequency representation. Both simulated and experimental results illustrate the adaptability and effectiveness of the proposed method.

The detection mechanism for false data injection attack via the ellipsoidal set‐membership approach

AbstractThe false data injection (FDI) attack detection problem in cyber‐physical systems (CPSs) is investigated in this paper. A novel attack detection algorithm is proposed based on the ellipsoidal set‐membership approach. In comparison to the existing FDI attack detection methods, the developed attack detection approach in this paper neither requires predefined thresholds nor specific statistical characteristics of the attacks. In order to guarantee that the estimation ellipsoid contains normal states despite the unknown but bounded (UBB) process and measurement noises, the one‐step ellipsoidal set‐membership estimation method is put forward. In addition, a convex optimization algorithm is introduced to calculate the gain matrix of the observer recursively. Moreover, with the help of the state estimation ellipsoid, the residual ellipsoid can be obtained for attack detection. Whether a detector can detect the FDI attack depends on the relationship between the residual value and residual ellipsoidal set. Finally, the effectiveness of the proposed method is demonstrated by a numerical simulation example.

Frequency-Domain Data-Driven Position-Dependent Controller Synthesis for Cartesian Robots

Cartesian robots have position-dependent dynamics that must be taken into account for high-performance applications. Traditional methods design linear time-invariant (LTI) controllers that are robustly stable with respect to position variations but result in reduced performance. Advanced methods require linear parameter varying (LPV) models and LPV controller design methods that are not well-established in the industry. On the other hand, the classical model-based gain-scheduled technique involves parametric identification, high-performance controller design for each position, interpolation of the controller parameters, and real-time controller validation, making it time-consuming and costly. Our approach uses frequency response at different operating points to design an LPV controller using a convex optimization algorithm based on second-order cone programming. The approach is applied to an industrial three-axis Cartesian robot, showing significant improvements over state-of-the-art control design strategies. Data acquisition and controller design can be performed automatically, reducing significantly the engineering costs for controller synthesis.

Joint-Transceiver Equalization Technique over a 1.4 km Multi-Mode Fiber Using Optical MIMO Technique in IM/DD Systems

In optical fiber communication, recent advances in multiple-input and multiple-output (MIMO) systems using space-division multiplexing have helped achieve higher spectral efficiency and data rates. Propagating higher-order modulation formats over MIMO systems further strengthens the capacity of the transmission link. In the optical-MIMO system, the dispersion impairments originating from a 1.4 km long multi-mode fiber (MMF) are mitigated using the proposed joint-transceiver equalization technique. A numerical convex optimization algorithm is used to compute and optimize the pre- and post-equalization (PPE) coefficients jointly restricted by cost and power budgets. The potential of the proposed joint-PPE technique is tested on an MMF link, which is severely degraded by dispersion compared to a single-mode fiber channel. From the experimental results, the average optical received power gain necessary to reach 10−4 bit-error rate is improved by nearly 2.5 dB using the joint-PPE compared to the post-equalization only based on the minimum mean-squared error principle. When the efficiency of the conventional zero-forcing (ZF) principle-based PPE and the joint-PPE is compared, the joint-PPE scheme outperforms the ZF-PPE by approximately 1.5 dB. The enhancement in the transmission quality is observed with experimentally measured eye diagrams using the joint-PPE scheme. Under the analyzed scenarios, computer simulation also confirms the hypothesis, which establishes the effectiveness of the proposed joint-transceiver equalization over the conventional ZF-PPE scheme. Moreover, the simulated performance benefits of the joint-PPE are evaluated using the singular value decomposition (SVD) technique. Improvement of ≈3.86 dB in the average optical received power gain required to reach 10−4 bit-error rate is witnessed with the PAM-4 format. Overall, the joint-transceiver equalization technique is proven to be beneficial in optical MIMO systems.

Observer-Based Fuzzy Control of Uncertain Nonlinear Singular Systems under Multi-Performance Requirements

This paper discusses an observer-based fuzzy control problem for uncertain nonlinear singular systems under Multi-Performance Requirements (MPRs). The approach used in the paper is to model the system using a Takagi–Sugeno (T-S) fuzzy model that can be analyzed using linear control theories. The proposed control scheme is based on the Parallel Distributed Compensation (PDC) approach and Proportional Derivative (PD) control scheme. The goal is to design an observer-based fuzzy controller that achieves stability of the system and also satisfies the Guarantee Cost Control (GCC) constraint while maintaining a desired passive constraint. The stability analysis is performed using Lyapunov theory, and the sufficient conditions are transformed into a Linear Matrix Inequality (LMI) form using a Shur Complement, free-weighting matrix method and Singular Value Decomposition (SVD) techniques. The LMI conditions are then solved using convex optimization algorithms. Finally, the proposed control method is validated using a bio-economic system to demonstrate its effectiveness.

Identification of Diffusively Coupled Linear Networks Through Structured Polynomial Models

Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are symmetric and therefore physical dynamic networks can be represented by undirected graphs. This paper shows how prediction error identification methods developed for linear time-invariant systems in polynomial form can be configured to consistently identify the parameters and the interconnection structure of diffusively coupled networks. Further, a multi-step least squares convex optimization algorithm is developed to solve the nonconvex optimization problem that results from the identification method.

Privacy-Preserving SGD on Shuffle Model

In this paper, we consider an exceptional study of differentially private stochastic gradient descent (SGD) algorithms in the stochastic convex optimization (SCO). The majority of the existing literature requires that the losses have additional assumptions, such as the loss functions with Lipschitz, smooth and strongly convex, and uniformly bounded of the model parameters, or focus on the Euclidean (i.e. l 2 d ) setting. However, these restrictive requirements exclude many popular losses, including the absolute loss and the hinge loss. By loosening the restrictions, we proposed two differentially private SGD without shuffle model and with shuffle model algorithms (in short, DP-SGD-NOS and DP-SGD-S) for the α , L -Hölder smooth loss by adding calibrated Laplace noise under no shuffling scheme and shuffling scheme in the l p d -setting for p ∈ 1,2 . We provide privacy guarantees by using advanced composition and privacy amplification techniques. We also analyze the convergence bounds of the DP-SGD-NOS and DP-SGD-S and obtain the optimal excess population risks O 1 / n + d log 1 / δ / n ϵ and O 1 / n + d log 1 / δ log n / δ / n 4 + α / 2 1 + α ϵ up to logarithmic factors with gradient complexity O n 2 − α / 1 + α + n . It turns out that the optimal utility bound with the shuffle model is superior to the bound without the shuffle model, which is consistent with the previous work. In addition, the DP-SGD-S achieves the optimal utility bound with the O n gradient computations of linearity for α ≥ 1 / 2 . There is a significant tradeoff between α , L -Hölder smooth losses and gradient complexity for differential privacy of SGD without shuffle model and with shuffle model.

Algorithm for evaluating distance-based entanglement measures

Abstract Quantifying entanglement in quantum systems is an important yet challenging task due to its NPhard nature. In this work, we propose an efficient algorithm for evaluating distance-based entanglement measures. Our approach builds on Gilbert’s algorithm for convex optimization, providing a reliable upper bound on the entanglement of a given arbitrary state. We demonstrate the effectiveness of our algorithm by applying it to various examples, such as calculating the squared Bures metric of entanglement as well as the relative entropy of entanglement for GHZ states, W states, Horodecki states, and chessboard states. These results demonstrate that our algorithm is a versatile and accurate tool that can quickly provide reliable upper bounds for entanglement measures.

Resource Allocation and Trajectory Optimization in OTFS-Based UAV-Assisted Mobile Edge Computing

Mobile edge computing (MEC) powered by unmanned aerial vehicles (UAVs), with the advantages of flexible deployment and wide coverage, is a promising technology to solve computationally intensive communication problems. In this paper, an orthogonal time frequency space (OTFS)-based UAV-assisted MEC system is studied, in which OTFS technology is used to mitigate the Doppler effect in UAV high-speed mobile communication. The weighted total energy consumption of the system is minimized by jointly optimizing the time division, CPU frequency allocation, transmit power allocation and flight trajectory while considering Doppler compensation. Thus, the resultant problem is a challenging nonconvex problem. We propose a joint algorithm that combines the benefits of the atomic orbital search (AOS) algorithm and convex optimization. Firstly, an improved AOS algorithm is proposed to swiftly obtain the time slot allocation and high-quality solution of the UAV optimal path. Secondly, the optimal solution for the CPU frequency and transmit power allocation is found by using Lagrangian duality and the first-order Taylor formula. Finally, the optimal solution of the original problem is iteratively obtained. The simulation results show that the weighted total energy consumption of the OTFS-based system decreases by 13.6% compared with the orthogonal frequency division multiplexing (OFDM)-based system. The weighted total energy consumption of the proposed algorithm decreases by 11.7% and 26.7% compared with convex optimization and heuristic algorithms, respectively.

A Spectral Encoding Simulator for Broadband Active Illumination and Reconstruction-Based Spectral Measurement

Spectral reflectance or transmittance measurements provide intrinsic information on the material of an object and are widely used in remote sensing, agriculture, diagnostic medicine, etc. Most reconstruction-based spectral reflectance or transmittance measurement methods based on broadband active illumination use narrow-band LEDs or lamps combined with specific filters as spectral encoding light sources. These light sources cannot achieve the designed spectral encoding with a high resolution and accuracy due to their low degree of freedom for adjustment, leading to inaccurate spectral measurements. To address this issue, we designed a spectral encoding simulator for active illumination. The simulator is composed of a prismatic spectral imaging system and a digital micromirror device. The spectral wavelengths and intensity are adjusted by switching the micromirrors. We used it to simulate spectral encodings according to the spectral distribution on micromirrors and solved the DMD patterns corresponding to the spectral encodings with a convex optimization algorithm. To verify the applicability of the simulator for spectral measurements based on active illumination, we used it to numerically simulate existing spectral encodings. We also numerically simulated a high-resolution Gaussian random measurement encoding for compressed sensing and measured the spectral reflectance of one vegetation type and two minerals through numerical simulations. We reconstructed the spectral transmittance of a calibrated filter through an experiment. The results show that the simulator can measure the spectral reflectance or transmittance with a high resolution and accuracy.

Multiband Pattern Synthesis of Time-Modulated Conformal Array with Quadratic Convex Optimization Algorithm

Aiming at the multiband pattern synthesis problem of time-modulated conformal array antenna, a quadratic convex optimization algorithm is proposed for sum and difference beamforming with low sidelobe levels. This articles method synthesizes a difference beam with a low sidelobe level by generating nulls at the center frequency band and optimizing the switch-on duration time of array elements. And the sum beamforming and sidelobe suppression of the first-order sideband are realized by optimizing the switch-on instant time of the array elements. The proposed algorithm has excellent properties of sidelobe suppression and angular sweep. The simulation results of circular and satellite array antenna verify the effectiveness of the algorithm.

Optimization Strategy of the Electric Vehicle Power Battery Based on the Convex Optimization Algorithm

With the development of the electric vehicle industry, electric vehicles have provided more choices for people. However, the performance of electric vehicles needs improvement, which makes most consumers take a wait-and-see attitude. Therefore, finding a method that can effectively improve the performance of electric vehicles is of great significance. To improve the current performance of electric vehicles, a convex optimization algorithm is proposed to optimize the motor model and power battery parameters of electric vehicles, improving the overall performance of electric vehicles. The performance of the proposed convex optimization algorithm, dual loop DP optimization algorithm, and nonlinear optimization algorithm is compared. The results show that the hydrogen consumption of electric vehicles optimized by the convex optimization algorithm is 95.364 g. This consumption is lower than 98.165 g of the DCDP optimization algorithm and 105.236 g of the nonlinear optimization algorithm before optimization. It is also significantly better than the 125.59 g of electric vehicles before optimization. The calculation time of the convex optimization algorithm optimization is 4.9 s, which is lower than the DCDP optimization algorithm and nonlinear optimization algorithm. The above results indicate that convex optimization algorithms have better optimization performance. After optimizing the power battery using a convex optimization algorithm, the overall performance of electric vehicles is higher. Therefore, this method can effectively improve the performance of current electric vehicle power batteries, make new energy vehicles develop rapidly, and improve the increasingly serious environmental pollution and energy crisis in China.