arXiv - MATH - Optimization and Control最新文献_第10页

A Unified Analysis of Saddle Flow Dynamics: Stability and Algorithm Design 鞍流动力学统一分析：稳定性与算法设计

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05290

Pengcheng You, Yingzhu Liu, Enrique Mallada

{"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}

引用次数: 0

A study on two-metric projection methods 关于两公制投影法的研究

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05321

Hanju Wu, Yue Xie

引用次数: 0

Carbon-Aware Quantification of Real-Time Aggregate Power Flexibility of Electric Vehicles 电动汽车实时总功率灵活性的碳感知量化

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05597

Xiaowei Wang, Yue Chen

{"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}

引用次数: 0

Complexity of Integer Programming in Reverse Convex Sets via Boundary Hyperplane Cover 通过边界超平面覆盖实现反凸集整数编程的复杂性

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05308

Robert Hildebrand, Adrian Göß

引用次数: 0

Tikhonov regularized inertial primal-dual dynamics for convex-concave bilinear saddle point problems 凸-凹双线性鞍点问题的梯霍诺夫正则化惯性初等-二元动力学

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05301

Xiangkai Sun, Liang He, Xian-Jun Long

引用次数: 0

RCM-Constrained Manipulator Trajectory Tracking Using Differential Kinematics Control 使用差分运动学控制的 RCM 受限机械手轨迹跟踪

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05740

Omar Rayyan, Vinicius Gonçalves, Nikolaos Evangeliou, Anthony Tzes

引用次数: 0

Continuous Relaxation of Discontinuous Shrinkage Operator: Proximal Inclusion and Conversion 非连续收缩算子的连续松弛：近端包容与转换

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05316

Masahiro Yukawa

引用次数: 0

Bridging Autoencoders and Dynamic Mode Decomposition for Reduced-order Modeling and Control of PDEs 衔接自动编码器和动态模式分解，实现 PDE 的降阶建模和控制

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.06101

Priyabrata Saha, Saibal Mukhopadhyay

引用次数: 0

Combining supervised learning and local search for the multicommodity capacitated fixed-charge network design problem 结合监督学习和局部搜索，解决多容性固定电荷网络设计问题

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05720

Charly Robinson La Rocca, Jean-François Cordeau, Emma Frejinger

{"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}

引用次数: 0

High-Precision Intelligent Reflecting Surfaces-assisted Positioning Service in 5G Networks with Flexible Numerology 采用灵活数字技术的 5G 网络高精度智能反射面辅助定位服务

arXiv - MATH - Optimization and Control Pub Date : 2024-09-09 DOI: arxiv-2409.05639

Ti Ti Nguyen, Kim-Khoa Nguyen

{"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}

引用次数: 0