arXiv - MATH - Optimization and Control最新文献_第8页

A Lagrangian shape and topology optimization framework based on semi-discrete optimal transport 基于半离散优化传输的拉格朗日形状和拓扑优化框架

arXiv - MATH - Optimization and Control Pub Date : 2024-09-12 DOI: arxiv-2409.07873

Charles Dapogny, Bruno Levy, Edouard Oudet

{"title":"A Lagrangian shape and topology optimization framework based on semi-discrete optimal transport","authors":"Charles Dapogny, Bruno Levy, Edouard Oudet","doi":"arxiv-2409.07873","DOIUrl":"https://doi.org/arxiv-2409.07873","url":null,"abstract":"This article revolves around shape and topology optimization, in the\u0000applicative context where the objective and constraint functionals depend on\u0000the solution to a physical boundary value problem posed on the optimized\u0000domain. We introduce a novel framework based on modern concepts from\u0000computational geometry, optimal transport and numerical analysis. Its pivotal\u0000feature is a representation of the optimized shape by the cells of an adapted\u0000version of a Laguerre diagram. Although such objects are originally described\u0000by a collection of seed points and weights, recent results from optimal\u0000transport theory suggest a more intuitive parametrization in terms of the seed\u0000points and measures of the associated cells. The polygonal mesh of the shape\u0000induced by this diagram serves as support for the deployment of the Virtual\u0000Element Method for the numerical solution of the physical boundary value\u0000problem at play and the calculation of the objective and constraint\u0000functionals. The sensitivities of the latter are derived next; at first, we\u0000calculate their derivatives with respect to the positions of the vertices of\u0000the Laguerre diagram by shape calculus techniques; a suitable adjoint\u0000methodology is then developed to express them in terms of the seed points and\u0000cell measures of the diagram. The evolution of the shape is realized by first\u0000updating the design variables according to these sensitivities and then\u0000reconstructing the diagram with efficient algorithms from computational\u0000geometry. Our shape optimization strategy is versatile: it can be applied to a\u0000wide gammut of physical situations. It is Lagrangian by essence, and it thereby\u0000benefits from all the assets of a consistently meshed representation of the\u0000shape. Yet, it naturally handles dramatic motions, including topological\u0000changes, in a very robust fashion. These features, among others, are\u0000illustrated by a series of 2d numerical examples.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212364","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

On time-inconsistent extended mean-field control problems with common noise 关于具有共同噪声的时间不一致扩展均场控制问题

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.07219

Zongxia Liang, Xiang Yu, Keyu Zhang

引用次数: 0

Two Decentralized Conjugate Gradient Methods with Global Convergence 两种具有全局收敛性的分散共轭梯度法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.07122

Liping Wang, Hao Wu, Hongchao Zhang

{"title":"Two Decentralized Conjugate Gradient Methods with Global Convergence","authors":"Liping Wang, Hao Wu, Hongchao Zhang","doi":"arxiv-2409.07122","DOIUrl":"https://doi.org/arxiv-2409.07122","url":null,"abstract":"This paper considers the decentralized optimization problem of minimizing a\u0000finite sum of continuously differentiable functions over a fixed-connected\u0000undirected network. Summarizing the lack of previously developed decentralized\u0000conjugate gradient methods, we propose two decentralized conjugate gradient\u0000method, called NDCG and DMBFGS respectively. Firstly, the best of our\u0000knowledge, NDCG is the first decentralized conjugate gradient method to be\u0000shown to have global convergence with constant stepsizes for general nonconvex\u0000optimization problems, which profits from our designed conjugate parameter and\u0000relies only on the same mild conditions as the centralized conjugate gradient\u0000method. Secondly, we apply the memoryless BFGS technique and develop the DMBFGS\u0000method. It requires only vector-vector products to capture the curvature\u0000information of Hessian matrices. Under proper choice of stepsizes, DMBFGS has\u0000global linear convergence for solving strongly convex decentralized\u0000optimization problems. Our numerical results show DMBFGS is very efficient\u0000compared with other state-of-the-art methods for solving decentralized\u0000optimization.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212392","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

Optimal Mechanisms for Demand Response: An Indifference Set Approach 需求响应的最佳机制：无偏见集方法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.07655

Mohammad Mehrabi, Omer Karaduman, Stefan Wager

{"title":"Optimal Mechanisms for Demand Response: An Indifference Set Approach","authors":"Mohammad Mehrabi, Omer Karaduman, Stefan Wager","doi":"arxiv-2409.07655","DOIUrl":"https://doi.org/arxiv-2409.07655","url":null,"abstract":"The time at which renewable (e.g., solar or wind) energy resources produce\u0000electricity cannot generally be controlled. In many settings, consumers have\u0000some flexibility in their energy consumption needs, and there is growing\u0000interest in demand-response programs that leverage this flexibility to shift\u0000energy consumption to better match renewable production -- thus enabling more\u0000efficient utilization of these resources. We study optimal demand response in a\u0000model where consumers operate home energy management systems (HEMS) that can\u0000compute the \"indifference set\" of energy-consumption profiles that meet\u0000pre-specified consumer objectives, receive demand-response signals from the\u0000grid, and control consumer devices within the indifference set. For example, if\u0000a consumer asks for the indoor temperature to remain between certain upper and\u0000lower bounds, a HEMS could time use of air conditioning or heating to align\u0000with high renewable production when possible. Here, we show that while\u0000price-based mechanisms do not in general achieve optimal demand response, i.e.,\u0000dynamic pricing cannot induce HEMS to choose optimal demand consumption\u0000profiles within the available indifference sets, pricing is asymptotically\u0000optimal in a mean-field limit with a growing number of consumers. Furthermore,\u0000we show that large-sample optimal dynamic prices can be efficiently derived via\u0000an algorithm that only requires querying HEMS about their planned consumption\u0000schedules given different prices. We demonstrate our approach in a grid\u0000simulation powered by OpenDSS, and show that it achieves meaningful demand\u0000response without creating grid instability.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212370","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

Two-Phase Optimization for PINN Training 针对 PINN 培训的两阶段优化

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.07296

Dimary Moreno López

引用次数: 0

An observability estimate for the wave equation and applications to the Neumann boundary controllability for semi-linear wave equations 波方程的可观测性估计及其在半线性波方程的诺伊曼边界可控性中的应用

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.07214

Sue Claret

引用次数: 0

Flexible block-iterative analysis for the Frank-Wolfe algorithm 弗兰克-沃尔夫算法的灵活分块迭代分析

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.06931

Gábor Braun, Sebastian Pokutta, Zev Woodstock

引用次数: 0

Exact SDP relaxations for a class of quadratic programs with finite and infinite quadratic constraints 具有有限和无限二次约束的一类二次方程程序的精确 SDP 放松

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.07213

Naohiko Arima, Sunyoung Kim, Masakazu Kojima

引用次数: 0

Constraining Genetic Symbolic Regression via Semantic Backpropagation 通过语义反向传播限制遗传符号回归

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.07369

Maximilian Reissmann, Yuan Fang, Andrew Ooi, Richard Sandberg

{"title":"Constraining Genetic Symbolic Regression via Semantic Backpropagation","authors":"Maximilian Reissmann, Yuan Fang, Andrew Ooi, Richard Sandberg","doi":"arxiv-2409.07369","DOIUrl":"https://doi.org/arxiv-2409.07369","url":null,"abstract":"Evolutionary symbolic regression approaches are powerful tools that can\u0000approximate an explicit mapping between input features and observation for\u0000various problems. However, ensuring that explored expressions maintain\u0000consistency with domain-specific constraints remains a crucial challenge. While\u0000neural networks are able to employ additional information like conservation\u0000laws to achieve more appropriate and robust approximations, the potential\u0000remains unrealized within genetic algorithms. This disparity is rooted in the\u0000inherent discrete randomness of recombining and mutating to generate new\u0000mapping expressions, making it challenging to maintain and preserve inferred\u0000constraints or restrictions in the course of the exploration. To address this\u0000limitation, we propose an approach centered on semantic backpropagation\u0000incorporated into the Gene Expression Programming (GEP), which integrates\u0000domain-specific properties in a vector representation as corrective feedback\u0000during the evolutionary process. By creating backward rules akin to algorithmic\u0000differentiation and leveraging pre-computed subsolutions, the mechanism allows\u0000the enforcement of any constraint within an expression tree by determining the\u0000misalignment and propagating desired changes back. To illustrate the\u0000effectiveness of constraining GEP through semantic backpropagation, we take the\u0000constraint of physical dimension as an example. This framework is applied to\u0000discovering physical equations from the Feynman lectures. Results have shown\u0000not only an increased likelihood of recovering the original equation but also\u0000notable robustness in the presence of noisy data.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212390","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

Riemannian Federated Learning via Averaging Gradient Stream 通过平均梯度流进行黎曼联盟学习

arXiv - MATH - Optimization and Control Pub Date : 2024-09-11 DOI: arxiv-2409.07223

Zhenwei Huang, Wen Huang, Pratik Jawanpuria, Bamdev Mishra

引用次数: 0