Geng Sun

Weijie Yuan, Yuanhao Cui, Jiacheng Wang et al.

In this article, we introduce a novel low-altitude wireless network (LAWN), which is a reconfigurable, three-dimensional (3D) layered architecture. In particular, the LAWN integrates connectivity, sensing, control, and computing across aerial and terrestrial nodes that enable seamless operation in complex, dynamic, and mission-critical environments. Different from the conventional aerial communication systems, LAWN's distinctive feature is its tight integration of functional planes in which multiple functionalities continually reshape themselves to operate safely and efficiently in the low-altitude sky. With the LAWN, we discuss several enabling technologies, such as integrated sensing and communication (ISAC), semantic communication, and fully-actuated control systems. Finally, we identify potential applications and key cross-layer challenges. This article offers a comprehensive roadmap for future research and development in the low-altitude airspace.

Jingru Zhu, Ya Guo, Geng Sun et al.

Semantic segmentation is a key technique involved in automatic interpretation of high-resolution remote sensing (HRS) imagery and has drawn much attention in the remote sensing community. Deep convolutional neural networks (DCNNs) have been successfully applied to the HRS imagery semantic segmentation task due to their hierarchical representation ability. However, the heavy dependency on a large number of training data with dense annotation and the sensitiveness to the variation of data distribution severely restrict the potential application of DCNNs for the semantic segmentation of HRS imagery. This study proposes a novel unsupervised domain adaptation semantic segmentation network (MemoryAdaptNet) for the semantic segmentation of HRS imagery. MemoryAdaptNet constructs an output space adversarial learning scheme to bridge the domain distribution discrepancy between source domain and target domain and to narrow the influence of domain shift. Specifically, we embed an invariant feature memory module to store invariant domain-level context information because the features obtained from adversarial learning only tend to represent the variant feature of current limited inputs. This module is integrated by a category attention-driven invariant domain-level context aggregation module to current pseudo invariant feature for further augmenting the pixel representations. An entropy-based pseudo label filtering strategy is used to update the memory module with high-confident pseudo invariant feature of current target images. Extensive experiments under three cross-domain tasks indicate that our proposed MemoryAdaptNet is remarkably superior to the state-of-the-art methods.

Xiaohua Ding, Hongyu Liu, Zaijiu Shang et al.

Based on reasonable testing model problems, we study the preservation by symplectic Runge-Kutta method (SRK) and symplectic partitioned Runge-Kutta method (SPRK) of structures for fixed points of linear Hamiltonian systems. The structure-preservation region provides a practical criterion for choosing step-size in symplectic computation. Examples are given to justify the investigation.

Geng Sun, Siqing Gan, Hongyu Liu et al.

Symmetric method and symplectic method are classical notions in the theory of Runge-Kutta methods. They can generate numerical flows that respectively preserve the symmetry and symplecticity of the continuous flows in the phase space. Adjoint method is an important way of constructing a new Runge-Kutta method via the symmetrisation of another Runge-Kutta method. In this paper, we introduce a new notion, called symplectic-adjoint Runge-Kutta method. We prove some interesting properties of the symmetric-adjoint and symplectic-adjoint methods. These properties reveal some intrinsic connections among several classical classes of Runge-Kutta methods. In particular, the newly introduced notion and the corresponding properties enable us to develop a novel and practical approach of constructing high-order explicit Runge-Kutta methods, which is a challenging and longly overlooked topic in the theory of Runge-Kutta methods.

Wenwen Xie, Geng Sun, Ruichen Zhang et al.

Integrated sensing and communication (ISAC) has emerged as a key development direction in the sixth-generation (6G) era, which provides essential support for the collaborative sensing and communication of future intelligent networks. However, as wireless environments become increasingly dynamic and complex, ISAC systems require more intelligent processing and more autonomous operation to maintain efficiency and adaptability. Meanwhile, agentic artificial intelligence (AI) offers a feasible solution to address these challenges by enabling continuous perception-reasoning-action loops in dynamic environments to support intelligent, autonomous, and efficient operation for ISAC systems. As such, we delve into the application value and prospects of agentic AI in ISAC systems in this work. Firstly, we provide a comprehensive review of agentic AI and ISAC systems to demonstrate their key characteristics. Secondly, we show several common optimization approaches for ISAC systems and highlight the significant advantages of generative artificial intelligence (GenAI)-based agentic AI. Thirdly, we propose a novel agentic ISAC framework and prensent a case study to verify its superiority in optimizing ISAC performance. Finally, we clarify future research directions for agentic AI-based ISAC systems.

Changyuan Zhao, Ruichen Zhang, Jiacheng Wang et al.

World models are emerging as a transformative paradigm in artificial intelligence, enabling agents to construct internal representations of their environments for predictive reasoning, planning, and decision-making. By learning latent dynamics, world models provide a sample-efficient framework that is especially valuable in data-constrained or safety-critical scenarios. In this paper, we present a comprehensive overview of world models, highlighting their architecture, training paradigms, and applications across prediction, generation, planning, and causal reasoning. We compare and distinguish world models from related concepts such as digital twins, the metaverse, and foundation models, clarifying their unique role as embedded cognitive engines for autonomous agents. We further propose Wireless Dreamer, a novel world model-based reinforcement learning framework tailored for wireless edge intelligence optimization, particularly in low-altitude wireless networks (LAWNs). Through a weather-aware UAV trajectory planning case study, we demonstrate the effectiveness of our framework in improving learning efficiency and decision quality.

Jingru Zhu, Ya Guo, Geng Sun et al.

Semantic segmentation of high-resolution remote sensing imagery (HRSI) suffers from the domain shift, resulting in poor performance of the model in another unseen domain. Unsupervised domain adaptive (UDA) semantic segmentation aims to adapt the semantic segmentation model trained on the labeled source domain to an unlabeled target domain. However, the existing UDA semantic segmentation models tend to align pixels or features based on statistical information related to labels in source and target domain data, and make predictions accordingly, which leads to uncertainty and fragility of prediction results. In this paper, we propose a causal prototype-inspired contrast adaptation (CPCA) method to explore the invariant causal mechanisms between different HRSIs domains and their semantic labels. It firstly disentangles causal features and bias features from the source and target domain images through a causal feature disentanglement module. Then, a causal prototypical contrast module is used to learn domain invariant causal features. To further de-correlate causal and bias features, a causal intervention module is introduced to intervene on the bias features to generate counterfactual unbiased samples. By forcing the causal features to meet the principles of separability, invariance and intervention, CPCA can simulate the causal factors of source and target domains, and make decisions on the target domain based on the causal features, which can observe improved generalization ability. Extensive experiments under three cross-domain tasks indicate that CPCA is remarkably superior to the state-of-the-art methods.

Yue Chen, Hui Kang, Jiahui Li et al.

The integration of simultaneous wireless information and power transfer (SWIPT) technology in 6G Internet of Things (IoT) networks faces significant challenges in remote areas and disaster scenarios where ground infrastructure is unavailable. This paper proposes a novel unmanned aerial vehicle (UAV)-assisted mobile edge computing (MEC) system enhanced by directional antennas to provide both computational resources and energy support for ground IoT terminals. However, such systems require multiple trade-off policies to balance UAV energy consumption, terminal battery levels, and computational resource allocation under various constraints, including limited UAV battery capacity, non-linear energy harvesting characteristics, and dynamic task arrivals. To address these challenges comprehensively, we formulate a bi-objective optimization problem that simultaneously considers system energy efficiency and terminal battery sustainability. We then reformulate this non-convex problem with a hybrid solution space as a Markov decision process (MDP) and propose an improved soft actor-critic (SAC) algorithm with an action simplification mechanism to enhance its convergence and generalization capabilities. Simulation results have demonstrated that our proposed approach outperforms various baselines in different scenarios, achieving efficient energy management while maintaining high computational performance. Furthermore, our method shows strong generalization ability across different scenarios, particularly in complex environments, validating the effectiveness of our designed boundary penalty and charging reward mechanisms.

Yinqiu Liu, Guangyuan Liu, Jiacheng Wang et al.

Nowadays, Generative AI (GenAI) reshapes numerous domains by enabling machines to create content across modalities. As GenAI evolves into autonomous agents capable of reasoning, collaboration, and interaction, they are increasingly deployed on network infrastructures to serve humans automatically. This emerging paradigm, known as the agentic network, presents new optimization challenges due to the demand to incorporate subjective intents of human users expressed in natural language. Traditional generic Deep Reinforcement Learning (DRL) struggles to capture intent semantics and adjust policies dynamically, thus leading to suboptimality. In this paper, we present LAMeTA, a Large AI Model (LAM)-empowered Two-stage Approach for intent-aware agentic network optimization. First, we propose Intent-oriented Knowledge Distillation (IoKD), which efficiently distills intent-understanding capabilities from resource-intensive LAMs to lightweight edge LAMs (E-LAMs) to serve end users. Second, we develop Symbiotic Reinforcement Learning (SRL), integrating E-LAMs with a policy-based DRL framework. In SRL, E-LAMs translate natural language user intents into structured preference vectors that guide both state representation and reward design. The DRL, in turn, optimizes the generative service function chain composition and E-LAM selection based on real-time network conditions, thus optimizing the subjective Quality-of-Experience (QoE). Extensive experiments conducted in an agentic network with 81 agents demonstrate that IoKD reduces mean squared error in intent prediction by up to 22.5%, while SRL outperforms conventional generic DRL by up to 23.5% in maximizing intent-aware QoE.

Xin Tang, Qian Chen, Wenjie Weng et al.

The integration of emerging uncrewed aerial vehicles (UAVs) with artificial intelligence (AI) and ground-embedded robots (GERs) has transformed emergency rescue operations in unknown environments. However, the high computational demands often exceed a single UAV's capacity, making it difficult to continuously provide stable high-level services. To address this, this paper proposes a cooperation framework involving UAVs, GERs, and airships. The framework enables resource pooling through UAV-to-GER (U2G) and UAV-to-airship (U2A) links, offering computing services for offloaded tasks. Specifically, we formulate the multi-objective problem of task assignment and exploration as a dynamic long-term optimization problem aiming to minimize task completion time and energy use while ensuring stability. Using Lyapunov optimization, we transform it into a per-slot deterministic problem and propose HG-MADDPG, which combines the Hungarian algorithm with a GDM-based multi-agent deep deterministic policy gradient. Simulations demonstrate significant improvements in offloading efficiency, latency, and system stability over baselines.

Zhang Liu, Dusit Niyato, Jiacheng Wang et al.

Lyapunov optimization theory has recently emerged as a powerful mathematical framework for solving complex stochastic optimization problems by transforming long-term objectives into a sequence of real-time short-term decisions while ensuring system stability. This theory is particularly valuable in unmanned aerial vehicle (UAV)-based low-altitude economy (LAE) networking scenarios, where it could effectively address inherent challenges of dynamic network conditions, multiple optimization objectives, and stability requirements. Recently, generative artificial intelligence (GenAI) has garnered significant attention for its unprecedented capability to generate diverse digital content. Extending beyond content generation, in this paper, we propose a framework integrating generative diffusion models with reinforcement learning to address Lyapunov optimization problems in UAV-based LAE networking. We begin by introducing the fundamentals of Lyapunov optimization theory and analyzing the limitations of both conventional methods and traditional AI-enabled approaches. We then examine various GenAI models and comprehensively analyze their potential contributions to Lyapunov optimization. Subsequently, we develop a Lyapunov-guided generative diffusion model-based reinforcement learning framework and validate its effectiveness through a UAV-based LAE networking case study. Finally, we outline several directions for future research.

Geng Sun, Weilong Ma, Jiahui Li et al.

The low-altitude economy (LAE), driven by unmanned aerial vehicles (UAVs) and other aircraft, has revolutionized fields such as transportation, agriculture, and environmental monitoring. In the upcoming six-generation (6G) era, UAV-assisted mobile edge computing (MEC) is particularly crucial in challenging environments such as mountainous or disaster-stricken areas. The computation task offloading problem is one of the key issues in UAV-assisted MEC, primarily addressing the trade-off between minimizing the task delay and the energy consumption of the UAV. In this paper, we consider a UAV-assisted MEC system where the UAV carries the edge servers to facilitate task offloading for ground devices (GDs), and formulate a calculation delay and energy consumption multi-objective optimization problem (CDECMOP) to simultaneously improve the performance and reduce the cost of the system. Then, by modeling the formulated problem as a multi-objective Markov decision process (MOMDP), we propose a multi-objective deep reinforcement learning (DRL) algorithm within an evolutionary framework to dynamically adjust the weights and obtain non-dominated policies. Moreover, to ensure stable convergence and improve performance, we incorporate a target distribution learning (TDL) algorithm. Simulation results demonstrate that the proposed algorithm can better balance multiple optimization objectives and obtain superior non-dominated solutions compared to other methods.

Zifan Lang, Guixia Liu, Geng Sun et al.

This paper proposes a UAV-assisted forwarding system based on distributed beamforming to enhance age of information (AoI) in Internet of Things (IoT). Specifically, UAVs collect and relay data between sensor nodes (SNs) and the remote base station (BS). However, flight delays increase the AoI and degrade the network performance. To mitigate this, we adopt distributed beamforming to extend the communication range, reduce the flight frequency and ensure the continuous data relay and efficient energy utilization. Then, we formulate an optimization problem to minimize AoI and UAV energy consumption, by jointly optimizing the UAV trajectories and communication schedules. The problem is non-convex and with high dynamic, and thus we propose a deep reinforcement learning (DRL)-based algorithm to solve the problem, thereby enhancing the stability and accelerate convergence speed. Simulation results show that the proposed algorithm effectively addresses the problem and outperforms other benchmark algorithms.

Zifan Lang, Guixia Liu, Geng Sun et al.

Despite the widespread deployment of terrestrial networks, providing reliable communication services to remote areas and maintaining connectivity during emergencies remains challenging. Low Earth orbit (LEO) satellite constellations offer promising solutions with their global coverage capabilities and reduced latency, yet struggle with intermittent coverage and limited communication windows due to orbital dynamics. This paper introduces an age of information (AoI)-aware space-air-ground integrated network (SAGIN) architecture that leverages a high-altitude platform (HAP) as intelligent relay between the LEO satellites and ground terminals. Our three-layer design employs hybrid free-space optical (FSO) links for high-capacity satellite-to-HAP communication and reliable radio frequency (RF) links for HAP-to-ground transmission, and thus addressing the temporal discontinuity in LEO satellite coverage while serving diverse user priorities. Specifically, we formulate a joint optimization problem to simultaneously minimize the AoI and satellite handover frequency through optimal transmit power distribution and satellite selection decisions. This highly dynamic, non-convex problem with time-coupled constraints presents significant computational challenges for traditional approaches. To address these difficulties, we propose a novel diffusion model (DM)-enhanced dueling double deep Q-network with action decomposition and state transformer encoder (DD3QN-AS) algorithm that incorporates transformer-based temporal feature extraction and employs a DM-based latent prompt generative module to refine state-action representations through conditional denoising. Simulation results highlight the superior performance of the proposed approach compared with policy-based methods and some other deep reinforcement learning (DRL) benchmarks.

Jiahui Li, Xinyue Liang, Geng Sun et al.

Low-altitude wireless networks (LAWNs) represent a promising architecture that integrates unmanned aerial vehicles (UAVs) as aerial nodes to provide enhanced coverage, reliability, and throughput for diverse applications. However, these networks face significant security vulnerabilities from both known and potential unknown eavesdroppers, which may threaten data confidentiality and system integrity. To solve this critical issue, we propose a novel secure communication framework for LAWNs where the selected UAVs within a swarm function as a virtual antenna array (VAA), complemented by intelligent reflecting surface (IRS) to create a robust defense against eavesdropping attacks. Specifically, we formulate a multi-objective optimization problem that simultaneously maximizes the secrecy rate while minimizing the maximum sidelobe level and total energy consumption, requiring joint optimization of UAV excitation current weights, flight trajectories, and IRS phase shifts. This problem presents significant difficulties due to the dynamic nature of the system and heterogeneous components. Thus, we first transform the problem into a heterogeneous Markov decision process (MDP). Then, we propose a heterogeneous multi-agent control approach (HMCA) that integrates a dedicated IRS control policy with a multi-agent soft actor-critic framework for UAV control, which enables coordinated operation across heterogeneous network elements. Simulation results show that the proposed HMCA achieves superior performance compared to baseline approaches in terms of secrecy rate improvement, sidelobe suppression, and energy efficiency. Furthermore, we find that the collaborative and passive beamforming synergy between VAA and IRS creates robust security guarantees when the number of UAVs increases.

Xinyue Liang, Hui Kang, Junwei Che et al.

While low-altitude wireless networks (LAWNs) based on uncrewed aerial vehicles (UAVs) offer high mobility, flexibility, and coverage for urban communications, they face severe signal attenuation in dense environments due to obstructions. To address this critical issue, we consider introducing collaborative beamforming (CB) of UAVs and omnidirectional reconfigurable beamforming (ORB) of simultaneous transmitting and reflecting reconfigurable intelligent surfaces (STAR-RIS) to enhance the signal quality and directionality. On this basis, we formulate a joint rate and energy optimization problem (JREOP) to maximize the transmission rate of the overall system, while minimizing the energy consumption of the UAV swarm. Due to the non-convex and NP-hard nature of JREOP, we propose a heterogeneous multi-agent collaborative dynamic (HMCD) optimization framework, which has two core components. The first component is a simulated annealing (SA)-based STAR-RIS control method, which dynamically optimizes reflection and transmission coefficients to enhance signal propagation. The second component is an improved multi-agent deep reinforcement learning (MADRL) control method, which incorporates a self-attention evaluation mechanism to capture interactions between UAVs and an adaptive velocity transition mechanism to enhance training stability. Simulation results demonstrate that HMCD outperforms various baselines in terms of convergence speed, average transmission rate, and energy consumption. Further analysis reveals that the average transmission rate of the overall system scales positively with both UAV count and STAR-RIS element numbers.

Weihong Qin, Aimin Wang, Geng Sun et al.

Space-air-ground integrated multi-access edge computing (SAGIN-MEC) provides a promising solution for the rapidly developing low-altitude economy (LAE) to deliver flexible and wide-area computing services. However, fully realizing the potential of SAGIN-MEC in the LAE presents significant challenges, including coordinating decisions across heterogeneous nodes with different roles, modeling complex factors such as mobility and network variability, and handling real-time decision-making under partially observable environment with hybrid variables. To address these challenges, we first present a hierarchical SAGIN-MEC architecture that enables the coordination between user devices (UDs), uncrewed aerial vehicles (UAVs), and satellites. Then, we formulate a UD cost minimization optimization problem (UCMOP) to minimize the UD cost by jointly optimizing the task offloading ratio, UAV trajectory planning, computing resource allocation, and UD association. We show that the UCMOP is an NP-hard problem. To overcome this challenge, we propose a multi-agent deep deterministic policy gradient (MADDPG)-convex optimization and coalitional game (MADDPG-COCG) algorithm. Specifically, we employ the MADDPG algorithm to optimize the continuous temporal decisions for heterogeneous nodes in the partially observable SAGIN-MEC system. Moreover, we propose a convex optimization and coalitional game (COCG) method to enhance the conventional MADDPG by deterministically handling the hybrid and varying-dimensional decisions. Simulation results demonstrate that the proposed MADDPG-COCG algorithm significantly enhances the user-centric performances in terms of the aggregated UD cost, task completion delay, and UD energy consumption, with a slight increase in UAV energy consumption, compared to the benchmark algorithms. Moreover, the MADDPG-COCG algorithm shows superior convergence stability and scalability.

Bowei Tong, Hui Kang, Jiahui Li et al.

Despite rapid advancements in sensor networks, conventional battery-powered sensor networks suffer from limited operational lifespans and frequent maintenance requirements that severely constrain their deployment in remote and inaccessible environments. As such, wireless rechargeable sensor networks (WRSNs) with mobile charging capabilities offer a promising solution to extend network lifetime. However, WRSNs face critical challenges from the inherent trade-off between maximizing the node survival rates and maximizing charging energy efficiency under dynamic operational conditions. In this paper, we investigate a typical scenario where mobile chargers move and charge the sensor, thereby maintaining the network connectivity while minimizing the energy waste. Specifically, we formulate a multi-objective optimization problem that simultaneously maximizes the network node survival rate and mobile charger energy usage efficiency across multiple time slots, which presents NP-hard computational complexity with long-term temporal dependencies that make traditional optimization approaches ineffective. To address these challenges, we propose an enhanced evolutionary multi-objective deep reinforcement learning algorithm, which integrates a long short-term memory (LSTM)-based policy network for temporal pattern recognition, a multilayer perceptron-based prospective increment model for future state prediction, and a time-varying Pareto policy evaluation method for dynamic preference adaptation. Extensive simulation results demonstrate that the proposed algorithm significantly outperforms existing approaches in balancing node survival rate and energy efficiency while generating diverse Pareto-optimal solutions. Moreover, the LSTM-enhanced policy network converges 25% faster than conventional networks, with the time-varying evaluation method effectively adapting to dynamic conditions.

Changyuan Zhao, Ruichen Zhang, Jiacheng Wang et al.

Self-evolving agentic artificial intelligence (AI) offers a new paradigm for future wireless systems by enabling autonomous agents to continually adapt and improve without human intervention. Unlike static AI models, self-evolving agents embed an autonomous evolution cycle that updates models, tools, and workflows in response to environmental dynamics. This paper presents a comprehensive overview of self-evolving agentic AI, highlighting its layered architecture, life cycle, and key techniques, including tool intelligence, workflow optimization, self-reflection, and evolutionary learning. We further propose a multi-agent cooperative self-evolving agentic AI framework, where multiple large language models (LLMs) are assigned role-specialized prompts under the coordination of a supervisor agent. Through structured dialogue, iterative feedback, and systematic validation, the system autonomously executes the entire life cycle without human intervention. A case study on antenna evolution in low-altitude wireless networks (LAWNs) demonstrates how the framework autonomously upgrades fixed antenna optimization into movable antenna optimization. Experimental results show that the proposed self-evolving agentic AI autonomously improves beam gain and restores degraded performance by up to 52.02%, consistently surpassing the fixed baseline with little to no human intervention and validating its adaptability and robustness for next-generation wireless intelligence.

Chuang Zhang, Geng Sun, Jiacheng Wang et al.

Low-altitude wireless networks (LAWNs) have the potential to revolutionize communications by supporting a range of applications, including urban parcel delivery, aerial inspections and air taxis. However, compared with traditional wireless networks, LAWNs face unique security challenges due to low-altitude operations, frequent mobility and reliance on unlicensed spectrum, making it more vulnerable to some malicious attacks. In this paper, we investigate some large artificial intelligence model (LAM)-enabled solutions for secure communications in LAWNs. Specifically, we first explore the amplified security risks and important limitations of traditional AI methods in LAWNs. Then, we introduce the basic concepts of LAMs and delve into the role of LAMs in addressing these challenges. To demonstrate the practical benefits of LAMs for secure communications in LAWNs, we propose a novel LAM-based optimization framework that leverages large language models (LLMs) to generate enhanced state features on top of handcrafted representations, and to design intrinsic rewards accordingly, thereby improving reinforcement learning performance for secure communication tasks. Through a typical case study, simulation results validate the effectiveness of the proposed framework. Finally, we outline future directions for integrating LAMs into secure LAWN applications.

Boyu Li, Kun He, Geng Sun

Anonymization technique has been extensively studied and widely applied for privacy-preserving data publishing. In most previous approaches, a microdata table consists of three categories of attribute: explicit-identifier, quasi-identifier (QI), and sensitive attribute. Actually, different individuals may have different view on the sensitivity of different attributes. Therefore, there is another type of attribute that contains both QI values and sensitive values, namely, semi-sensitive attribute. Based on such observation, we propose a new anonymization technique, called local generalization and bucketization, to prevent identity disclosure and protect the sensitive values on each semi-sensitive attribute and sensitive attribute. The rationale is to use local generalization and local bucketization to divide the tuples into local equivalence groups and partition the sensitive values into local buckets, respectively. The protections of local generalization and local bucketization are independent, so that they can be implemented by appropriate algorithms without weakening other protection, respectively. Besides, the protection of local bucketization for each semi-sensitive attribute and sensitive attribute is also independent. Consequently, local bucketization can comply with various principles in different attributes according to the actual requirements of anonymization. The conducted extensive experiments illustrate the effectiveness of the proposed approach.

Xin-long Luo, Jia-hui Lv, Geng Sun

This paper investigates the localization problem of high-speed high-altitude unmanned aerial vehicle (UAV) with a monocular camera and inertial navigation system. It proposes a navigation method utilizing the complementarity of vision and inertial devices to overcome the singularity which arises from the horizontal flight of UAV. Furthermore, it modifies the mathematical model of localization problem via separating linear parts from nonlinear parts and replaces a nonlinear least-squares problem with a linearly equality-constrained optimization problem. In order to avoid the ill-condition property near the optimal point of sequential unconstrained minimization techniques(penalty methods), it constructs a semi-implicit continuous method with a trust-region technique based on a differential-algebraic dynamical system to solve the linearly equality-constrained optimization problem. It also analyzes the global convergence property of the semi-implicit continuous method in an infinity integrated interval other than the traditional convergence analysis of numerical methods for ordinary differential equations in a finite integrated interval. Finally, the promising numerical results are also presented.

Xin-Long Luo, Geng Sun

This article explores some geometric and algebraic properties of the dynamical system which is represented by matrix differential equations arising from inertial navigation problems, such as the symplecticity and the orthogonality. Furthermore, it extends the applicable fields of symplectic geometric algorithms from the even dimensional Hamiltonian system to the odd dimensional dynamical system. Finally, some numerical experiments are presented and illustrate the theoretical results of this paper.