Convex Optimization Method Research Articles

A modified inertial three-term conjugate gradient method for nonsmooth convex optimization and its application

A modified inertial three-term conjugate gradient method for nonsmooth convex optimization and its application

A Parameter Estimation-Based Anti-Deception Jamming Method for RIS-Aided Single-Station Radar

Multi-station radar can provide better performance against deception jamming, but the harsh detection requirements and risk of network destruction undermine the practicability of the multi-station radar. Therefore, it is necessary to further explore the anti-deception jamming performance of a single-station radar. This paper introduces a novel method, based on parameter estimation with a virtual multi-station system, to discriminate range deceptive jamming. The system consists of a single-station radar assisted by the reconfigurable intelligent surfaces (RIS). A unified parameter estimation model for true and false targets is established, and the convex optimization method is applied to estimate the target location and deception range. The Cramer–Rao lower bound (CRLB) of the target localization and the measured deception range is then derived. By using the measured deception range and its CRLB, an optimal discrimination algorithm in accordance with the Neyman–Pearson lemma is designed. Simulation results demonstrate the feasibility of the proposed method and analyze the effects of factors such as signal-to-noise ratio (SNR), deception range, jammer location, and the RISs station arrangement on the discrimination performance.

On Some Works of Boris Teodorovich Polyak on the Convergence of Gradient Methods and Their Development

The paper presents a review of the current state of subgradient and accelerated convex optimization methods, including the cases with the presence of noise and access to various information about the objective function (function value, gradient, stochastic gradient, higher derivatives). For nonconvex problems, the Polyak–Lojasiewicz condition is considered and a review of the main results is given. The behavior of numerical methods in the presence of a sharp minimum is considered. The aim of this review is to show the influence of the works of B.T. Polyak (1935–2023) on gradient optimization methods and their surroundings on the modern development of numerical optimization methods.

Buffer Occupancy-Based Congestion Control Protocol for Wireless Multimedia Sensor Networks

Wireless multimedia sensor networks (WMSNs) have stringent constraints and need to deliver data packets to the sink node within a predefined limited time. However, due to congestion, buffer overflow occurs and leads to the degradation of the quality-of-service (QoS) parameters of event information. Congestion in WMSNs results in exhausted node energy, degraded network performance, increased transmission delays, and high packet loss. Congestion occurs when the volume of data trying to pass through a network exceeds its capacity. First, the BOCC protocol uses two congestion indicators to detect congestion. One is the buffer occupancy and other is the buffer occupancy change rate. Second, a rate controller is proposed to protect high-priority I-frame packets during congestion. BOCC sends a congestion notification to the source node to reduce congestion in the network. The source node adjusts its data transmission rate after receiving the congestion notification message. In the proposed algorithm, the rate adjustment is made by discarding low-priority P-frame packets from the source nodes. Third, to further improve the performance of the BOCC protocol, the problem is formulated as a constrained optimization problem and solved using convex optimization and sequential quadratic programming (SQP) methods. Experimental results based on Raspberry Pi sensor nodes show that the BOCC protocol achieves up to 16% reduction in packet loss and up to 23% reduction in average end-to-end delay compared to state-of-the-art congestion control algorithms.

Topology optimization of multi-material structures subjected to dynamic loads

Traditional designs for multi-material structures are mostly based on static loads. However, engineering structures are often subjected to dynamic loads. This paper firstly and systematically conducts an in-depth study on the topological design of multi-material structures under dynamic loads. In this method, the definition of design variable adopts the ordered solid isotropic material with penalization (ordered-SIMP) method to normalize the design variable, without introducing any additional variables, the HHT-α method is employed to solve the dynamic optimization problem. To address the dynamic optimization problems with constraints on mass and cost, a convex optimization method based on the concept of sensitivity separation is used to update the design variables, and search for the structural topologies. Finally, this paper provides some numerical examples with respect to time-varying, material parameters, load amplitude, load direction and multiple loads, to discuss in depth the topological and numerical results of these examples.

Super-Resolution Reconstruction of Remote Sensing Images Using Chaotic Mapping to Optimize Sparse Representation.

Current super-resolution algorithms exhibit limitations when processing noisy remote sensing images rich in surface information, as they tend to amplify noise during the recovery of high-frequency signals. To mitigate this issue, this paper presents a novel approach that incorporates the concept of compressed sensing and explores the super-resolution problem of remote sensing images for space cameras, particularly for high-speed imaging systems. The proposed algorithm employs K-singular value decomposition (K-SVD) to jointly train high- and low-resolution image blocks, updating them column by column to obtain overcomplete dictionary pairs. This approach compensates for the deficiency of fixed dictionaries in the original algorithm. In the process of dictionary updating, we innovatively integrate the circle chaotic mapping into the solution process of the dictionary sequence, replacing pseudorandom numbers. This integration facilitates balanced traversal and simplifies the search for global optimal solutions. For the optimization problem of sparse coefficients, we utilize the orthogonal matching pursuit method (OMP) instead of the L1 norm convex optimization method used in most reconstruction techniques, thereby complementing the K-SVD dictionary update algorithm. After upscaling and denoising the image using the dictionary pair mapping relationship, we further emphasize image edge details with local gradients as constraints. When compared with various representative super-resolution algorithms, our algorithm effectively filters out noise and stains in low-resolution images. It not only performs well visually but also stands out in objective evaluation indicators such as the peak signal-to-noise ratio and information entropy. The experimental results validate the effectiveness of the proposed method in super-resolution remote sensing images, yielding high-quality remote sensing image data.

Distributed Generation Approach with Helping of Charging Stations

This study addresses the optimization difficulties created by the combination of distributed generation (DG) and charging stations (CS), with the key difference that charging stations not only permit electric vehicle charging but also actively contribute to power supply. Using Convex Optimization (CVX) methods, the study formulates and solves optimization issues for coordinating and controlling DG units, taking into account charging stations' dual roles as power suppliers. The findings indicate that EVs can significantly contribute to grid stability, but challenges such as battery degradation and the need for advanced battery management systems (BMS) must be addressed to optimize these benefits. Simulation results show a potential improvement in grid stability the promise and the practical considerations of this innovative approach.

A Convex Optimization Method to Time-Optimal Trajectory Planning With Jerk Constraint for Industrial Robotic Manipulators

A Convex Optimization Method to Time-Optimal Trajectory Planning With Jerk Constraint for Industrial Robotic Manipulators

Cluster synchronization of complex dynamic networks under pinning control via a limited capacity communication channel

In this paper, the cluster synchronization pinning control problem is investigated for the continuous-time-directed complex dynamic networks under the bit rate constraint. Firstly, a node selection scheme based on differences in node degrees is proposed to achieve cluster synchronization. Subsequently, a coding–decoding scheme is designed during data transmission through digital communication channels where only a limited number of encoded signal sequences are sent to the controller side. Further, regarding the unreliability of the channel, the phenomenon of packet dropouts is considered during the encoding process, which is modeled by using a series of independent Bernoulli distributed random variables. The pinning controller is then designed based on the received decoding information. By means of the convex optimization method, a sufficient condition is established to ensure that the cluster synchronization error is ultimately bounded and the desired controller gain is determined based on the solution to matrix inequalities. Finally, the effectiveness of the obtained results is validated through a simulation example.

Adaptive pseudospectral successive convex optimization for six-degree-of-freedom powered descent guidance

Guidance for six-degrees-of-freedom powered descent is more challenging due to its stronger nonlinearity compared to three-degrees-of-freedom. The standard convex programming algorithm has been difficult to effectively address this problem. To enhance the performance of successive convex programming in terms of both optimality and accuracy, an adaptive pseudospectral successive convex optimization algorithm is proposed in this paper. First, it transforms the nonlinear optimal control problem into a convex subproblem by integrating global pseudospectral discretization with local linearization. Second, a parameter-adaptive successive convexification algorithm is proposed, which adaptively adjusts the trust region size based on the update rate of the optimal trajectory. Last, the global error and local error are accurately calculated based on the pseudospectral method. To tackle the issue of excessively large local errors caused by nonlinearity, an adaptive grid method is proposed to refine the mesh grid. Simulation results demonstrate the efficacy of the proposed pseudospectral convex optimization method and adaptive mesh grid method in reducing local errors and improving solution accuracy. Furthermore, the proposed parameter-adaptive successive convex optimization algorithm exhibits adaptability and optimality across different initial conditions, while also improving solution accuracy.

A feasible smoothing accelerated projected gradient method for nonsmooth convex optimization

Smoothing accelerated gradient methods achieve faster convergence rates than that of the subgradient method for some nonsmooth convex optimization problems. However, Nesterov's extrapolation may require gradients at infeasible points, and thus they cannot be applied to some structural optimization problems. We introduce a variant of smoothing accelerated projected gradient methods where every variable is feasible. The O(k−1log⁡k) convergence rate is obtained using the Lyapunov function. We conduct a numerical experiment on the robust compliance optimization of a truss structure.

Powered–coasting–powered multi-phase mission reconfiguration method for launch vehicles under power system failures

For the final stage of a launch vehicle with powered–coasting–powered multi-phase flight, this paper investigates the joint reconfiguration method to determine subsequent flight trajectory and degraded orbit after power system failure in the first powered phase. While power system failures due to mass–flow–rate drop have been thoroughly studied in the existing literature, this paper focuses on the more challenging specific impulse drop failures, which result in loss of total launcher energy. This paper aims to design a fault-tolerant guidance method with onboard potential and to analyze the survivability and characteristics of the launcher in the event of such a failure. In the problem modeling, the strong nonlinearity of the orbital elements as terminal constraints is eliminated by analyzing the orbital properties in the orbital coordinate system to establish the primal trajectory optimization problem. For this multi-phase trajectory optimization problem, a joint optimization algorithm for the degradation orbit and the flight trajectory, based on convex optimization and Radau pseudospectral method, is designed to achieve autonomous mission reconfiguration. The algorithm introduces the relaxation–penalization idea, where the terminal constraints are relaxed and penalized in the performance index, allowing the algorithm to adaptively form an optimal degradation circular or elliptical orbit based on the remaining capacity of the launch vehicle. Simulation experiments demonstrate the effectiveness and superiority of the mission reconfiguration algorithm. Finally, the paper presents the first analysis of the optimal allocation of flight time between the first powered phase, the coasting phase, and the second powered phase in a propellant depletion scenario following the launcher power system failure.

Trajectory optimization for aerodynamically controlled missiles by chance-constrained sequential convex programming

The flight environment of aerodynamically controlled missiles is full of complexity and uncertainty. To cope with the uncertainty more effectively and enhance the convergence performance in trajectory optimization problems for aerodynamically controlled missiles simultaneously, the chance-constrained sequential convex programming (CC-SCP) algorithm is proposed in this paper. The uncertainty is regarded as the chance constraint, and a smooth and differential approximation function is designed to transform this chance constraint into the constraint that the convex optimization method can handle. Subsequently, the originally non-convex trajectory optimization problem is reformulated into a series of convex optimization subproblems, in which an initial reference trajectory guess generation strategy is proposed, and a theoretical proof of the exact convex relaxation is given to enhance the algorithm's convergence performance and theoretical value, respectively. Numerical simulations are provided to verify the convergence and effectiveness of the CC-SCP algorithm, and the advantages of using the CC-SCP algorithm to cope with the uncertainty are illustrated. Furthermore, comparative simulation examples show that the proposed algorithm possesses a low conservatism, which means the proposed algorithm can obtain a bigger convergence region and a better solution than other current methods when handling the same chance constraints. Finally, the robustness of the algorithm is discussed.

Two-Tier Efficient QoE Optimization for Partitioning and Resource Allocation in UAV-Assisted MEC.

Unmanned aerial vehicles (UAVs) have increasingly become integral to multi-access edge computing (MEC) due to their flexibility and cost-effectiveness, especially in the B5G and 6G eras. This paper aims to enhance the quality of experience (QoE) in large-scale UAV-MEC networks by minimizing the shrinkage ratio through optimal decision-making in computation mode selection for each user device (UD), UAV flight trajectory, bandwidth allocation, and computing resource allocation at edge servers. However, the interdependencies among UAV trajectory, binary task offloading mode, and computing/network resource allocation across numerous IoT nodes pose significant challenges. To address these challenges, we formulate the shrinkage ratio minimization problem as a mixed-integer nonlinear programming (MINLP) problem and propose a two-tier optimization strategy. To reduce the scale of the optimization problem, we first design a low-complexity UAV partition coverage algorithm based on the Welzl method and determine the UAV flight trajectory by solving a traveling salesman problem (TSP). Subsequently, we develop a coordinate descent (CD)-based method and an alternating direction method of multipliers (ADMM)-based method for network bandwidth and computing resource allocation in the MEC system. Extensive simulations demonstrate that the CD-based method is simple to implement and highly efficient in large-scale UAV-MEC networks, reducing the time complexity by three orders of magnitude compared to convex optimization methods. Meanwhile, the ADMM-based joint optimization method achieves approximately an 8% reduction in shrinkage ratio optimization compared to baseline methods.

A robust joint frequency spectrum and power allocation strategy in a coexisting radar and communication system

The resource allocation technique is of great significance in achieving frequency spectrum coexistence in Joint Radar-Communication (JRC) systems, by which the problem of radio frequency spectrum congestion can be well alleviated. A Robust Joint Frequency Spectrum and Power Allocation (RJFSPA) strategy is proposed for the Coexisting Radar and Communication (CRC) system. Specifically, we consider the uncertainty of target Radar Cross Section (RCS) and communication channel gain to formulate a bi-objective optimization model. The joint probabilities that the Cramér-Rao Lower Bound (CRLB) of each target satisfying the localization accuracy threshold and the Communication Data Ratio (CDR) of each user satisfying the communication threshold are simultaneously maximized, under the constraint of the total power budget. A Three-Stage Alternating Optimization Method (TSAOM) is proposed to obtain the Best-Known Pareto Subset (BK-PS) of this problem, where the frequency spectrum, radar power, and communicator power are allocated using the greedy search and standard convex optimization methods, respectively. Simulation results confirm the effectiveness of the proposed RJFSPA strategy, compared with the resource allocation methods in a uniform manner and that ignores the uncertainties. The efficiency of the TSAOM is also verified by the comparison with the exhaustive search-based method.

A High-Precision Hand-Eye Coordination Localization Method under Convex Relaxation Optimization.

Traditional switching operations require on-site work, and the high voltage generated by arc discharges can pose a risk of injury to the operator. Therefore, a combination of visual servo and robot control is used to localize the switching operation and construct hand-eye calibration equations. The solution to the hand-eye calibration equations is coupled with the rotation matrix and translation vectors, and it depends on the initial value determination. This article presents a convex relaxation global optimization hand-eye calibration algorithm based on dual quaternions. Firstly, the problem model is simplified using the mathematical tools of dual quaternions, and then the linear matrix inequality convex optimization method is used to obtain a rotation matrix with higher accuracy. Afterwards, the calibration equations of the translation vectors are rewritten, and a new objective function is established to solve the coupling influence between them, maintaining positioning precision at approximately 2.9 mm. Considering the impact of noise on the calibration process, Gaussian noise is added to the solutions of the rotation matrix and translation vector to make the data more closely resemble the real scene in order to evaluate the performance of different hand-eye calibration algorithms. Eventually, an experiment comparing different hand-eye calibration methods proves that the proposed algorithm is better than other hand-eye calibration algorithms in terms of calibration accuracy, robustness to noise, and stability, satisfying the accuracy requirements of switching operations.

Intelligent Online Offloading and Resource Allocation for HAP Drones and Satellite Collaborative Networks

High-altitude platform (HAP) drones and satellites collaborate to form a network that provides edge computing services to terrestrial internet of things (IoT) devices, which is considered a promising method. In this network, IoT devices’ tasks can be split into multiple parts and processed by servers at non-terrestrial nodes in different locations, thereby reducing task processing delays. However, splitting tasks and allocating communication and computing resources are important challenges. In this paper, we investigate the task offloading and resource allocation problem in multi-HAP drones and multi-satellite collaborative networks. In particular, we formulate a task splitting and communication and computing resource optimization problem to minimize the total delay of all IoT devices’ tasks. To solve this problem, we first transform and decompose the original problem into two subproblems. We design a task splitting optimization algorithm based on deep reinforcement learning, which can achieve online task offloading decision-making. This algorithm structurally designs the actor network to ensure that output actions are always valid. Furthermore, we utilize convex optimization methods to optimize the resource allocation subproblem. The simulation results show that our algorithm can effectively converge and significantly reduce the total task processing delay when compared with other baseline algorithms.

Reconfigurable Intelligent Surface Assisted Target Three-Dimensional Localization with 2-D Radar

Battlefield surveillance radar is usually 2-D radar, which cannot realize target three-dimensional localization, leading to poor resolution for the air target in the elevation dimension. Previous researchers have used the Traditional Height Finder Radar (HFR) or multiple 2-D radar networking to estimate the target three-dimensional location. However, all of them face the problems of high cost, poor real-time performance and high requirement of space–time registration. In this paper, Reconfigurable Intelligent Surfaces (RISs) with low cost are introduced into the 2-D radar to realize the target three-dimensional localization. Taking advantage of the wide beam of 2-D radar in the elevation dimension, several Unmanned Aerial Vehicles (UAVs) carrying RISs are set in the receiving beam to form multiple auxiliary measurement channels. In addition, the traditional 2-D radar measurements combined with the auxiliary channel measurements are used to realize the target three-dimensional localization by solving a nonlinear least square problem with a convex optimization method. For the proposed RIS-assisted target three-dimensional localization problem, the Cramer–Rao Lower Bound (CRLB) is derived to measure the target localization accuracy. Simulation results verify the effectiveness of the proposed 3-D localization method, and the influences of the number, the positions and the site errors of the RISs on the localization accuracy are covered.

Dictionary-Based Multi-View Learning With Privileged Information

Multi-view learning can improve classification performance by combining information between different views. Due to the similarity in different views of the dataset, sometimes the features obtained are highly limited and redundant. At the same time, different views accumulate a large amount of noisy information, which will affect the classification performance of the model. To solve these problems, we embed privileged information in the model and introduce dictionary learning, and proposed a new dictionary-based multi-view learning method with privileged information (MVDL-PI). First, two sets of dictionaries (synthetic dictionary and analysis dictionary) and sparse representation matrices of different information domains are obtained for each view information and privilege information through dictionary learning. Then, we obtain consistency information from the regularization terms of the two different sets of synthetic dictionaries and construct a LUPI (Learning using privileged information) classifier by the sparse representation. In addition, we use alternating convex optimization and Lagrange multiplier methods to optimize the model and prove its convergence. In the experiment, we did a number of experiments comparing this method with similar recent methods. The experimental results show that the MVDL-PI method is superior to other methods in terms of stability and classification accuracy.

Fast Pattern Synthesis for Large-Scale Time-Modulated Planar Arrays With a Novel Two-Stage Iterative Convex Optimization Method

Fast Pattern Synthesis for Large-Scale Time-Modulated Planar Arrays With a Novel Two-Stage Iterative Convex Optimization Method