arXiv - MATH - Optimization and Control最新文献_第6页

A kernel-based PEM estimator for forward model 基于核的前向模型 PEM 估计器

arXiv - MATH - Optimization and Control Pub Date : 2024-09-15 DOI: arxiv-2409.09679

Giulio Fattore, Marco Peruzzo, Giacomo Sartori, Mattia Zorzi

引用次数: 0

Lossy Image Compression with Stochastic Quantization 利用随机量化技术压缩有损图像

arXiv - MATH - Optimization and Control Pub Date : 2024-09-14 DOI: arxiv-2409.09488

Anton Kozyriev, Vladimir Norkin

{"title":"Lossy Image Compression with Stochastic Quantization","authors":"Anton Kozyriev, Vladimir Norkin","doi":"arxiv-2409.09488","DOIUrl":"https://doi.org/arxiv-2409.09488","url":null,"abstract":"Lossy image compression algorithms play a crucial role in various domains,\u0000including graphics, and image processing. As image information density\u0000increases, so do the resources required for processing and transmission. One of\u0000the most prominent approaches to address this challenge is color quantization,\u0000proposed by Orchard et al. (1991). This technique optimally maps each pixel of\u0000an image to a color from a limited palette, maintaining image resolution while\u0000significantly reducing information content. Color quantization can be\u0000interpreted as a clustering problem (Krishna et al. (1997), Wan (2019)), where\u0000image pixels are represented in a three-dimensional space, with each axis\u0000corresponding to the intensity of an RGB channel. However, scaling of\u0000traditional algorithms like K-Means can be challenging for large data, such as\u0000modern images with millions of colors. This paper reframes color quantization\u0000as a three-dimensional stochastic transportation problem between the set of\u0000image pixels and an optimal color palette, where the number of colors is a\u0000predefined hyperparameter. We employ Stochastic Quantization (SQ) with a\u0000seeding technique proposed by Arthur et al. (2007) to enhance the scalability\u0000of color quantization. This method introduces a probabilistic element to the\u0000quantization process, potentially improving efficiency and adaptability to\u0000diverse image characteristics. To demonstrate the efficiency of our approach,\u0000we present experimental results using images from the ImageNet dataset. These\u0000experiments illustrate the performance of our Stochastic Quantization method in\u0000terms of compression quality, computational efficiency, and scalability\u0000compared to traditional color quantization techniques.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254546","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

Initial Error Affection and Error Correction in Linear Quadratic Mean Field Games under Erroneous Initial Information 错误初始信息下线性二次均场博弈中的初始错误情感和错误纠正

arXiv - MATH - Optimization and Control Pub Date : 2024-09-14 DOI: arxiv-2409.09375

Yuxin Jin, Lu Ren, Wang Yao, Xiao Zhang

引用次数: 0

Observability inequalities for heat equations with potentials 有势热方程的可观测性不等式

arXiv - MATH - Optimization and Control Pub Date : 2024-09-14 DOI: arxiv-2409.09476

Jiuyi Zhu, Jinping Zhuge

引用次数: 0

Addressing Discrete Dynamic Optimization via a Logic-Based Discrete-Steepest Descent Algorithm 通过基于逻辑的离散陡坡下降算法解决离散动态优化问题

arXiv - MATH - Optimization and Control Pub Date : 2024-09-14 DOI: arxiv-2409.09237

Zedong Peng, Albert Lee, David E. Bernal Neira

{"title":"Addressing Discrete Dynamic Optimization via a Logic-Based Discrete-Steepest Descent Algorithm","authors":"Zedong Peng, Albert Lee, David E. Bernal Neira","doi":"arxiv-2409.09237","DOIUrl":"https://doi.org/arxiv-2409.09237","url":null,"abstract":"Dynamic optimization problems involving discrete decisions have several\u0000applications, yet lead to challenging optimization problems that must be\u0000addressed efficiently. Combining discrete variables with potentially nonlinear\u0000constraints stemming from dynamics within an optimization model results in\u0000mathematical programs for which off-the-shelf techniques might be insufficient.\u0000This work uses a novel approach, the Logic-based Discrete-Steepest Descent\u0000Algorithm (LD-SDA), to solve Discrete Dynamic Optimization problems. The\u0000problems are formulated using Boolean variables that enforce differential\u0000systems of constraints and encode logic constraints that the optimization\u0000problem needs to satisfy. By posing the problem as a generalized disjunctive\u0000program with dynamic equations within the disjunctions, the LD-SDA takes\u0000advantage of the problem's inherent structure to efficiently explore the\u0000combinatorial space of the Boolean variables and selectively include relevant\u0000differential equations to mitigate the computational complexity inherent in\u0000dynamic optimization scenarios. We rigorously evaluate the LD-SDA with\u0000benchmark problems from the literature that include dynamic transitioning modes\u0000and find it to outperform traditional methods, i.e., mixed-integer nonlinear\u0000and generalized disjunctive programming solvers, in terms of efficiency and\u0000capability to handle dynamic scenarios. This work presents a systematic method\u0000and provides an open-source software implementation to address these discrete\u0000dynamic optimization problems by harnessing the information within its\u0000logical-differential structure.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254552","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 Adaptive Control of Linear Stochastic Systems with Quadratic Cost Function 具有二次成本函数的线性随机系统的最优自适应控制

arXiv - MATH - Optimization and Control Pub Date : 2024-09-14 DOI: arxiv-2409.09250

Nian Liu, Cheng Zhao, Shaolin Tan, Jinhu Lü

{"title":"Optimal Adaptive Control of Linear Stochastic Systems with Quadratic Cost Function","authors":"Nian Liu, Cheng Zhao, Shaolin Tan, Jinhu Lü","doi":"arxiv-2409.09250","DOIUrl":"https://doi.org/arxiv-2409.09250","url":null,"abstract":"In this paper, we consider the adaptive linear quadratic Gaussian control\u0000problem, where both the linear transformation matrix of the state $A$ and the\u0000control gain matrix $B$ are unknown. The proposed adaptive optimal control only\u0000assumes that $(A, B)$ is stabilizable and $(A, Q^{1/2})$ is detectable, where\u0000$Q$ is the weighting matrix of the state in the quadratic cost function. This\u0000condition significantly weakens the classic assumptions used in the literature.\u0000To tackle this problem, a weighted least squares algorithm is modified by using\u0000random regularization method, which can ensure uniform stabilizability and\u0000uniform detectability of the family of estimated models. At the same time, a\u0000diminishing excitation is incorporated into the design of the proposed adaptive\u0000control to guarantee strong consistency of the desired components of the\u0000estimates. Finally, by utilizing this family of estimates, even if not all\u0000components of them converge to the true values, it is demonstrated that a\u0000certainty equivalence control with such a diminishing excitation is optimal for\u0000an ergodic quadratic cost function.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254550","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

Constraints-Informed Neural-Laguerre Approximation of Nonlinear MPC with Application in Power Electronics 非线性 MPC 的约束条件神经-拉盖尔逼近法在电力电子技术中的应用

arXiv - MATH - Optimization and Control Pub Date : 2024-09-14 DOI: arxiv-2409.09436

Duo Xu, Rody Aerts, Petros Karamanakos, Mircea Lazar

{"title":"Constraints-Informed Neural-Laguerre Approximation of Nonlinear MPC with Application in Power Electronics","authors":"Duo Xu, Rody Aerts, Petros Karamanakos, Mircea Lazar","doi":"arxiv-2409.09436","DOIUrl":"https://doi.org/arxiv-2409.09436","url":null,"abstract":"This paper considers learning online (implicit) nonlinear model predictive\u0000control (MPC) laws using neural networks and Laguerre functions. Firstly, we\u0000parameterize the control sequence of nonlinear MPC using Laguerre functions,\u0000which typically yields a smoother control law compared to the original\u0000nonlinear MPC law. Secondly, we employ neural networks to learn the\u0000coefficients of the Laguerre nonlinear MPC solution, which comes with several\u0000benefits, namely the dimension of the learning space is dictated by the number\u0000of Laguerre functions and the complete predicted input sequence can be used to\u0000learn the coefficients. To mitigate constraints violation for neural\u0000approximations of nonlinear MPC, we develop a constraints-informed loss\u0000function that penalizes the violation of polytopic state constraints during\u0000learning. Box input constraints are handled by using a clamp function in the\u0000output layer of the neural network. We demonstrate the effectiveness of the\u0000developed framework on a nonlinear buck-boost converter model with sampling\u0000rates in the sub-millisecond range, where online nonlinear MPC would not be\u0000able to run in real time. The developed constraints-informed neural-Laguerre\u0000approximation yields similar performance with long-horizon online nonlinear\u0000MPC, but with execution times of a few microseconds, as validated on a\u0000field-programmable gate array (FPGA) platform.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254596","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

New Heuristics for the Operation of an Ambulance Fleet under Uncertainty 不确定情况下救护车队运行的新启发式方法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-13 DOI: arxiv-2409.09158

Vincent Guigues, Anton J. Kleywegt, Victor Hugo Nascimento

{"title":"New Heuristics for the Operation of an Ambulance Fleet under Uncertainty","authors":"Vincent Guigues, Anton J. Kleywegt, Victor Hugo Nascimento","doi":"arxiv-2409.09158","DOIUrl":"https://doi.org/arxiv-2409.09158","url":null,"abstract":"The operation of an ambulance fleet involves ambulance selection decisions\u0000about which ambulance to dispatch to each emergency, and ambulance reassignment\u0000decisions about what each ambulance should do after it has finished the service\u0000associated with an emergency. For ambulance selection decisions, we propose\u0000four new heuristics: the Best Myopic (BM) heuristic, a NonMyopic (NM)\u0000heuristic, and two greedy heuristics (GHP1 and GHP2). Two variants of the\u0000greedy heuristics are also considered. We also propose an optimization problem\u0000for an extension of the BM heuristic, useful when a call for several patients\u0000arrives. For ambulance reassignment decisions, we propose several strategies to\u0000choose which emergency in queue to send an ambulance to or which ambulance\u0000station to send an ambulance to when it finishes service. These heuristics are\u0000also used in a rollout approach: each time a new decision has to be made (when\u0000a call arrives or when an ambulance finishes service), a two-stage stochastic\u0000program is solved. The proposed heuristics are used to efficiently compute the\u0000second stage cost of these problems. We apply the rollout approach with our\u0000heuristics to data of the Emergency Medical Service (EMS) of a large city, and\u0000show that these methods outperform other heuristics that have been proposed for\u0000ambulance dispatch decisions. We also show that better response times can be\u0000obtained using the rollout approach instead of using the heuristics without\u0000rollout. Moreover, each decision is computed in a few seconds, which allows\u0000these methods to be used for the real-time management of a fleet of ambulances.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254553","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 Unified Funnel Restoration SQP Algorithm 统一的漏斗恢复 SQP 算法

arXiv - MATH - Optimization and Control Pub Date : 2024-09-13 DOI: arxiv-2409.09208

David Kiessling, Sven Leyffer, Charlie Vanaret

引用次数: 0

Convergence rate of opinion dynamics with complex interaction types 具有复杂互动类型的舆论动态收敛率

arXiv - MATH - Optimization and Control Pub Date : 2024-09-13 DOI: arxiv-2409.09100

Lingling Yao, Aming Li

{"title":"Convergence rate of opinion dynamics with complex interaction types","authors":"Lingling Yao, Aming Li","doi":"arxiv-2409.09100","DOIUrl":"https://doi.org/arxiv-2409.09100","url":null,"abstract":"The convergence rate is a crucial issue in opinion dynamics, which\u0000characterizes how quickly opinions reach a consensus and tells when the\u0000collective behavior can be formed. However, the key factors that determine the\u0000convergence rate of opinions are elusive, especially when individuals interact\u0000with complex interaction types such as friend/foe, ally/adversary, or\u0000trust/mistrust. In this paper, using random matrix theory and low-rank\u0000perturbation theory, we present a new body of theory to comprehensively study\u0000the convergence rate of opinion dynamics. First, we divide the complex\u0000interaction types into five typical scenarios: mutual trust $(+/+)$, mutual\u0000mistrust $(-/-)$, trust$/$mistrust $(+/-)$, unilateral trust $(+/0)$, and\u0000unilateral mistrust $(-/0)$. For diverse interaction types, we derive the\u0000mathematical expression of the convergence rate, and further establish the\u0000direct connection between the convergence rate and population size, the density\u0000of interactions (network connectivity), and individuals' self-confidence level.\u0000Second, taking advantage of these connections, we prove that for the $(+/+)$,\u0000$(+/-)$, $(+/0)$, and random mixture of different interaction types, the\u0000convergence rate is proportional to the population size and network\u0000connectivity, while it is inversely proportional to the individuals'\u0000self-confidence level. However, for the $(-/-)$ and $(-/0)$ scenarios, we draw\u0000the exact opposite conclusions. Third, for the $(+/+,-/-)$ and $(-/-,-/0)$\u0000scenarios, we derive the optimal proportion of different interaction types to\u0000ensure the fast convergence of opinions. Finally, simulation examples are\u0000provided to illustrate the effectiveness and robustness of our theoretical\u0000findings.","PeriodicalId":501286,"journal":{"name":"arXiv - MATH - Optimization and Control","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142254592","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