This work examines the conditions for asymptotic and exponential convergence of saddle flow dynamics of convex-concave functions. First, we propose an observability-based certificate for asymptotic convergence, directly bridging the gap between the invariant set in a LaSalle argument and the equilibrium set of saddle flows. This certificate generalizes conventional conditions for convergence, e.g., strict convexity-concavity, and leads to a novel state-augmentation method that requires minimal assumptions for asymptotic convergence. We also show that global exponential stability follows from strong convexity-strong concavity, providing a lower-bound estimate of the convergence rate. This insight also explains the convergence of proximal saddle flows for strongly convex-concave objective functions. Our results generalize to dynamics with projections on the vector field and have applications in solving constrained convex optimization via primal-dual methods. Based on these insights, we study four algorithms built upon different Lagrangian function transformations. We validate our work by applying these methods to solve a network flow optimization and a Lasso regression problem.
{"title":"A Unified Analysis of Saddle Flow Dynamics: Stability and Algorithm Design","authors":"Pengcheng You, Yingzhu Liu, Enrique Mallada","doi":"arxiv-2409.05290","DOIUrl":"https://doi.org/arxiv-2409.05290","url":null,"abstract":"This work examines the conditions for asymptotic and exponential convergence\u0000of saddle flow dynamics of convex-concave functions. First, we propose an\u0000observability-based certificate for asymptotic convergence, directly bridging\u0000the gap between the invariant set in a LaSalle argument and the equilibrium set\u0000of saddle flows. This certificate generalizes conventional conditions for\u0000convergence, e.g., strict convexity-concavity, and leads to a novel\u0000state-augmentation method that requires minimal assumptions for asymptotic\u0000convergence. We also show that global exponential stability follows from strong\u0000convexity-strong concavity, providing a lower-bound estimate of the convergence\u0000rate. This insight also explains the convergence of proximal saddle flows for\u0000strongly convex-concave objective functions. Our results generalize to dynamics\u0000with projections on the vector field and have applications in solving\u0000constrained convex optimization via primal-dual methods. Based on these\u0000insights, we study four algorithms built upon different Lagrangian function\u0000transformations. We validate our work by applying these methods to solve a\u0000network flow optimization and a Lasso regression problem.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212435","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The two-metric projection method is a simple yet elegant algorithm proposed by Bertsekas in 1984 to address bound/box-constrained optimization problems. The algorithm's low per-iteration cost and potential for using Hessian information makes it a favourable computation method for this problem class. However, its global convergence guarantee is not studied in the nonconvex regime. In our work, we first investigate the global complexity of such a method for finding first-order stationary solution. After properly scaling each step, we equip the algorithm with competitive complexity guarantees. Furthermore, we generalize the two-metric projection method for solving $ell_1$-norm minimization and discuss its properties via theoretical statements and numerical experiments.
{"title":"A study on two-metric projection methods","authors":"Hanju Wu, Yue Xie","doi":"arxiv-2409.05321","DOIUrl":"https://doi.org/arxiv-2409.05321","url":null,"abstract":"The two-metric projection method is a simple yet elegant algorithm proposed\u0000by Bertsekas in 1984 to address bound/box-constrained optimization problems.\u0000The algorithm's low per-iteration cost and potential for using Hessian\u0000information makes it a favourable computation method for this problem class.\u0000However, its global convergence guarantee is not studied in the nonconvex\u0000regime. In our work, we first investigate the global complexity of such a\u0000method for finding first-order stationary solution. After properly scaling each\u0000step, we equip the algorithm with competitive complexity guarantees.\u0000Furthermore, we generalize the two-metric projection method for solving\u0000$ell_1$-norm minimization and discuss its properties via theoretical\u0000statements and numerical experiments.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Electric vehicles (EVs) can be aggregated to offer flexibility services to the power system. However, the rapid growth in EV adoption leads to increased grid-level carbon emissions due to higher EV charging demand, complicating grid decarbonization efforts. Quantifying and managing EV flexibility while controlling carbon emissions is crucial. This paper introduces a methodology for carbon-aware quantification of real-time aggregate EV power flexibility. An offline model is first developed to determine the upper and lower bounds of the EV flexibility region. To address uncertainties in EV charging behaviors and grid carbon intensity, we propose a carbon-aware online optimization algorithm based on Lyapunov optimization, incorporating a queue model to capture system dynamics. To enhance EV flexibility, we integrate dispatch signals from the system operator into the queue update through a two-stage disaggregation process. The proposed approach is prediction-free and adaptable to various uncertainties. Additionally, the maximum charging delay for EV charging tasks is theoretically bounded by a constant, and carbon emissions are effectively controlled. Numerical results demonstrate the effectiveness of the proposed online method and highlight its advantages over several benchmarks through comparisons.
{"title":"Carbon-Aware Quantification of Real-Time Aggregate Power Flexibility of Electric Vehicles","authors":"Xiaowei Wang, Yue Chen","doi":"arxiv-2409.05597","DOIUrl":"https://doi.org/arxiv-2409.05597","url":null,"abstract":"Electric vehicles (EVs) can be aggregated to offer flexibility services to\u0000the power system. However, the rapid growth in EV adoption leads to increased\u0000grid-level carbon emissions due to higher EV charging demand, complicating grid\u0000decarbonization efforts. Quantifying and managing EV flexibility while\u0000controlling carbon emissions is crucial. This paper introduces a methodology\u0000for carbon-aware quantification of real-time aggregate EV power flexibility. An\u0000offline model is first developed to determine the upper and lower bounds of the\u0000EV flexibility region. To address uncertainties in EV charging behaviors and\u0000grid carbon intensity, we propose a carbon-aware online optimization algorithm\u0000based on Lyapunov optimization, incorporating a queue model to capture system\u0000dynamics. To enhance EV flexibility, we integrate dispatch signals from the\u0000system operator into the queue update through a two-stage disaggregation\u0000process. The proposed approach is prediction-free and adaptable to various\u0000uncertainties. Additionally, the maximum charging delay for EV charging tasks\u0000is theoretically bounded by a constant, and carbon emissions are effectively\u0000controlled. Numerical results demonstrate the effectiveness of the proposed\u0000online method and highlight its advantages over several benchmarks through\u0000comparisons.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212428","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We study the complexity of identifying the integer feasibility of reverse convex sets. We present various settings where the complexity can be either NP-Hard or efficiently solvable when the dimension is fixed. Of particular interest is the case of bounded reverse convex constraints with a polyhedral domain. We introduce a structure, emph{Boundary Hyperplane Cover}, that permits this problem to be solved in polynomial time in fixed dimension provided the number of nonlinear reverse convex sets is fixed.
{"title":"Complexity of Integer Programming in Reverse Convex Sets via Boundary Hyperplane Cover","authors":"Robert Hildebrand, Adrian Göß","doi":"arxiv-2409.05308","DOIUrl":"https://doi.org/arxiv-2409.05308","url":null,"abstract":"We study the complexity of identifying the integer feasibility of reverse\u0000convex sets. We present various settings where the complexity can be either\u0000NP-Hard or efficiently solvable when the dimension is fixed. Of particular\u0000interest is the case of bounded reverse convex constraints with a polyhedral\u0000domain. We introduce a structure, emph{Boundary Hyperplane Cover}, that\u0000permits this problem to be solved in polynomial time in fixed dimension\u0000provided the number of nonlinear reverse convex sets is fixed.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212434","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, for a convex-concave bilinear saddle point problem, we propose a Tikhonov regularized second-order primal-dual dynamical system with slow damping, extrapolation and general time scaling parameters. Depending on the vanishing speed of the rescaled regularization parameter (i.e., the product of Tikhonov regularization parameter and general time scaling parameter), we analyze the convergence properties of the trajectory generated by the dynamical system. When the rescaled regularization parameter decreases rapidly to zero, we obtain convergence rates of the primal-dual gap and velocity vector along the trajectory generated by the dynamical system. In the case that the rescaled regularization parameter tends slowly to zero, we show the strong convergence of the trajectory towards the minimal norm solution of the convex-concave bilinear saddle point problem. Further, we also present some numerical experiments to illustrate the theoretical results.
{"title":"Tikhonov regularized inertial primal-dual dynamics for convex-concave bilinear saddle point problems","authors":"Xiangkai Sun, Liang He, Xian-Jun Long","doi":"arxiv-2409.05301","DOIUrl":"https://doi.org/arxiv-2409.05301","url":null,"abstract":"In this paper, for a convex-concave bilinear saddle point problem, we propose\u0000a Tikhonov regularized second-order primal-dual dynamical system with slow\u0000damping, extrapolation and general time scaling parameters. Depending on the\u0000vanishing speed of the rescaled regularization parameter (i.e., the product of\u0000Tikhonov regularization parameter and general time scaling parameter), we\u0000analyze the convergence properties of the trajectory generated by the dynamical\u0000system. When the rescaled regularization parameter decreases rapidly to zero,\u0000we obtain convergence rates of the primal-dual gap and velocity vector along\u0000the trajectory generated by the dynamical system. In the case that the rescaled\u0000regularization parameter tends slowly to zero, we show the strong convergence\u0000of the trajectory towards the minimal norm solution of the convex-concave\u0000bilinear saddle point problem. Further, we also present some numerical\u0000experiments to illustrate the theoretical results.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Omar Rayyan, Vinicius Gonçalves, Nikolaos Evangeliou, Anthony Tzes
This paper proposes an approach for controlling surgical robotic systems, while complying with the Remote Center of Motion (RCM) constraint in Robot-Assisted Minimally Invasive Surgery (RA-MIS). In this approach, the RCM-constraint is upheld algorithmically, providing flexibility in the positioning of the insertion point and enabling compatibility with a wide range of general-purpose robots. The paper further investigates the impact of the tool's insertion ratio on the RCM-error, and introduces a manipulability index of the robot which considers the RCM-error that it is used to find a starting configuration. To accurately evaluate the proposed method's trajectory tracking within an RCM-constrained environment, an electromagnetic tracking system is employed. The results demonstrate the effectiveness of the proposed method in addressing the RCM constraint problem in RA-MIS.
{"title":"RCM-Constrained Manipulator Trajectory Tracking Using Differential Kinematics Control","authors":"Omar Rayyan, Vinicius Gonçalves, Nikolaos Evangeliou, Anthony Tzes","doi":"arxiv-2409.05740","DOIUrl":"https://doi.org/arxiv-2409.05740","url":null,"abstract":"This paper proposes an approach for controlling surgical robotic systems,\u0000while complying with the Remote Center of Motion (RCM) constraint in\u0000Robot-Assisted Minimally Invasive Surgery (RA-MIS). In this approach, the\u0000RCM-constraint is upheld algorithmically, providing flexibility in the\u0000positioning of the insertion point and enabling compatibility with a wide range\u0000of general-purpose robots. The paper further investigates the impact of the\u0000tool's insertion ratio on the RCM-error, and introduces a manipulability index\u0000of the robot which considers the RCM-error that it is used to find a starting\u0000configuration. To accurately evaluate the proposed method's trajectory tracking\u0000within an RCM-constrained environment, an electromagnetic tracking system is\u0000employed. The results demonstrate the effectiveness of the proposed method in\u0000addressing the RCM constraint problem in RA-MIS.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212468","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We present a principled way of deriving a continuous relaxation of a given discontinuous shrinkage operator, which is based on a couple of fundamental results. First, the image of a point with respect to the ``set-valued'' proximity operator of a nonconvex function is included by that for its lower semicontinuous (l.s.c.) 1-weakly-convex envelope. Second, the ``set-valued'' proximity operator of a proper l.s.c. 1-weakly-convex function is converted, via double inversion, to a ``single-valued'' proximity operator which is Lipschitz continuous. As a specific example, we derive a continuous relaxation of the discontinuous shrinkage operator associated with the reversely ordered weighted $ell_1$ (ROWL) penalty. Numerical examples demonstrate potential advantages of the continuous relaxation.
{"title":"Continuous Relaxation of Discontinuous Shrinkage Operator: Proximal Inclusion and Conversion","authors":"Masahiro Yukawa","doi":"arxiv-2409.05316","DOIUrl":"https://doi.org/arxiv-2409.05316","url":null,"abstract":"We present a principled way of deriving a continuous relaxation of a given\u0000discontinuous shrinkage operator, which is based on a couple of fundamental\u0000results. First, the image of a point with respect to the ``set-valued''\u0000proximity operator of a nonconvex function is included by that for its lower\u0000semicontinuous (l.s.c.) 1-weakly-convex envelope. Second, the ``set-valued''\u0000proximity operator of a proper l.s.c. 1-weakly-convex function is converted,\u0000via double inversion, to a ``single-valued'' proximity operator which is\u0000Lipschitz continuous. As a specific example, we derive a continuous relaxation\u0000of the discontinuous shrinkage operator associated with the reversely ordered\u0000weighted $ell_1$ (ROWL) penalty. Numerical examples demonstrate potential\u0000advantages of the continuous relaxation.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212432","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Modeling and controlling complex spatiotemporal dynamical systems driven by partial differential equations (PDEs) often necessitate dimensionality reduction techniques to construct lower-order models for computational efficiency. This paper explores a deep autoencoding learning method for reduced-order modeling and control of dynamical systems governed by spatiotemporal PDEs. We first analytically show that an optimization objective for learning a linear autoencoding reduced-order model can be formulated to yield a solution closely resembling the result obtained through the dynamic mode decomposition with control algorithm. We then extend this linear autoencoding architecture to a deep autoencoding framework, enabling the development of a nonlinear reduced-order model. Furthermore, we leverage the learned reduced-order model to design controllers using stability-constrained deep neural networks. Numerical experiments are presented to validate the efficacy of our approach in both modeling and control using the example of a reaction-diffusion system.
{"title":"Bridging Autoencoders and Dynamic Mode Decomposition for Reduced-order Modeling and Control of PDEs","authors":"Priyabrata Saha, Saibal Mukhopadhyay","doi":"arxiv-2409.06101","DOIUrl":"https://doi.org/arxiv-2409.06101","url":null,"abstract":"Modeling and controlling complex spatiotemporal dynamical systems driven by\u0000partial differential equations (PDEs) often necessitate dimensionality\u0000reduction techniques to construct lower-order models for computational\u0000efficiency. This paper explores a deep autoencoding learning method for\u0000reduced-order modeling and control of dynamical systems governed by\u0000spatiotemporal PDEs. We first analytically show that an optimization objective\u0000for learning a linear autoencoding reduced-order model can be formulated to\u0000yield a solution closely resembling the result obtained through the dynamic\u0000mode decomposition with control algorithm. We then extend this linear\u0000autoencoding architecture to a deep autoencoding framework, enabling the\u0000development of a nonlinear reduced-order model. Furthermore, we leverage the\u0000learned reduced-order model to design controllers using stability-constrained\u0000deep neural networks. Numerical experiments are presented to validate the\u0000efficacy of our approach in both modeling and control using the example of a\u0000reaction-diffusion system.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212400","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Charly Robinson La Rocca, Jean-François Cordeau, Emma Frejinger
The multicommodity capacitated fixed-charge network design problem has been extensively studied in the literature due to its wide range of applications. Despite the fact that many sophisticated solution methods exist today, finding high-quality solutions to large-scale instances remains challenging. In this paper, we explore how a data-driven approach can help improve upon the state of the art. By leveraging machine learning models, we attempt to reveal patterns hidden in the data that might be difficult to capture with traditional optimization methods. For scalability, we propose a prediction method where the machine learning model is called at the level of each arc of the graph. We take advantage of off-the-shelf models trained via supervised learning to predict near-optimal solutions. Our experimental results include an algorithm design analysis that compares various integration strategies of predictions within local search algorithms. We benchmark the ML-based approach with respect to the state-of-the-art heuristic for this problem. The findings indicate that our method can outperform the leading heuristic on sets of instances sampled from a uniform distribution.
由于应用范围广泛，文献中对多容性固定电荷网络设计问题进行了广泛研究。尽管目前存在许多复杂的求解方法，但要为大规模实例找到高质量的解决方案仍然具有挑战性。在本文中，我们将探讨数据驱动方法如何帮助改善现有技术水平。通过利用机器学习模型，我们试图揭示隐藏在数据中的模式，而传统的优化方法可能很难捕捉到这些模式。为了提高可扩展性，我们提出了一种预测方法，在这种方法中，机器学习模型是在图的每个弧的层次上调用的。我们利用通过监督学习训练的现成模型来预测接近最优的解决方案。我们的实验结果包括算法设计分析，该分析比较了本地搜索算法中的各种预测集成策略。我们将基于 ML 的方法与最先进的启发式方法进行了比较。研究结果表明，在从均匀分布中抽样的实例集上，我们的方法优于领先的启发式方法。
{"title":"Combining supervised learning and local search for the multicommodity capacitated fixed-charge network design problem","authors":"Charly Robinson La Rocca, Jean-François Cordeau, Emma Frejinger","doi":"arxiv-2409.05720","DOIUrl":"https://doi.org/arxiv-2409.05720","url":null,"abstract":"The multicommodity capacitated fixed-charge network design problem has been\u0000extensively studied in the literature due to its wide range of applications.\u0000Despite the fact that many sophisticated solution methods exist today, finding\u0000high-quality solutions to large-scale instances remains challenging. In this\u0000paper, we explore how a data-driven approach can help improve upon the state of\u0000the art. By leveraging machine learning models, we attempt to reveal patterns\u0000hidden in the data that might be difficult to capture with traditional\u0000optimization methods. For scalability, we propose a prediction method where the\u0000machine learning model is called at the level of each arc of the graph. We take\u0000advantage of off-the-shelf models trained via supervised learning to predict\u0000near-optimal solutions. Our experimental results include an algorithm design\u0000analysis that compares various integration strategies of predictions within\u0000local search algorithms. We benchmark the ML-based approach with respect to the\u0000state-of-the-art heuristic for this problem. The findings indicate that our\u0000method can outperform the leading heuristic on sets of instances sampled from a\u0000uniform distribution.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212409","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Accurate positioning is paramount for a wide array of location-based services (LBS) in fifth-generation (5G) wireless networks. Recent advances in 5G New Radio (NR) technology holds promise for very high-precision positioning services. Yet, challenges arise due to diverse types of numerology and massive connected devices. This paper presents a novel approach to improve positioning precision within a 5G NR framework with comb patterns on time-frequency resource mapping. We then formulate an optimization problem aimed at minimizing the maximum users' positioning error in an intelligent reflected surface (IRS)-assisted 5G network by controlling the user-anchor association, numerology-related selection, IRS's reflecting elements, privacy protection level, and transmit power. To address the non-convex nature of the underlying mixed-integer non-convex problem (MINLP), we propose an efficient algorithm that combines optimization, matching, and learning techniques. Through extensive numerical experiments, we demonstrate the effectiveness of our proposed algorithm in minimizing positioning errors compared to conventional methods.
在第五代（5G）无线网络中，精确定位对各种基于位置的服务（LBS）至关重要。5G 新无线电（NR）技术的最新进展为提供高精度定位服务带来了希望。然而，由于数字类型的多样性和海量连接设备，挑战也随之而来。本文提出了一种在 5G NR 框架内利用时频资源映射梳理模式提高定位精度的新方法。然后，我们提出了一个优化问题，旨在通过控制用户-锚点关联、数字相关选择、IRS 的反射元素、隐私保护级别和发射功率，最小化智能反射面（IRS）辅助 5G 网络中用户的最大定位误差。针对底层混合整数非凸问题（MINLP）的非凸性质，我们提出了一种结合优化、匹配和学习技术的高效算法。通过大量的数值实验，我们证明了与传统方法相比，我们提出的算法在最小化定位误差方面的有效性。
{"title":"High-Precision Intelligent Reflecting Surfaces-assisted Positioning Service in 5G Networks with Flexible Numerology","authors":"Ti Ti Nguyen, Kim-Khoa Nguyen","doi":"arxiv-2409.05639","DOIUrl":"https://doi.org/arxiv-2409.05639","url":null,"abstract":"Accurate positioning is paramount for a wide array of location-based services\u0000(LBS) in fifth-generation (5G) wireless networks. Recent advances in 5G New\u0000Radio (NR) technology holds promise for very high-precision positioning\u0000services. Yet, challenges arise due to diverse types of numerology and massive\u0000connected devices. This paper presents a novel approach to improve positioning\u0000precision within a 5G NR framework with comb patterns on time-frequency\u0000resource mapping. We then formulate an optimization problem aimed at minimizing\u0000the maximum users' positioning error in an intelligent reflected surface\u0000(IRS)-assisted 5G network by controlling the user-anchor association,\u0000numerology-related selection, IRS's reflecting elements, privacy protection\u0000level, and transmit power. To address the non-convex nature of the underlying\u0000mixed-integer non-convex problem (MINLP), we propose an efficient algorithm\u0000that combines optimization, matching, and learning techniques. Through\u0000extensive numerical experiments, we demonstrate the effectiveness of our\u0000proposed algorithm in minimizing positioning errors compared to conventional\u0000methods.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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