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14th IFAC conference on Control applications in Marine Systems, Robotics, and Vehicles (CAMS)

作者： Odven, Petter K. Martinsen, Andreas B. Lekkas, Anastasios M. Norwegian Univ Sci & Technol NTNU Dept Engn Cybernet NO-7491 Trondheim Norway Kongsberg Maritime Horten Norway

Docking operations for autonomous surface vehicles (ASVs) involve challenges related to low-speed maneuvering in confined harbour spaces while handling environmental forces and traffic. Recently, optimization-based docking approaches have demonstrated promising results in unobstructed convex harbor areas, however they are still limited in dealing with static obstacles, which adds the significant challenge of non-convex constraints. In this paper, we present two hybrid methods that addresses the problem of docking while avoiding both static and dynamic obstacles that obstruct the direct path to the quay. The first phase involves the utilization of computational geometry for partitioning the non-convex harbor area into convex polygons. Then, a search algorithm computes the optimal sequence of convex polygons that connect the starting pose to the docking pose in an obstacle-free manner. Finally, trajectory planning is achieved via numerical optimal control. In this way, the proposed methods helps avoiding local minima and preserves the benefits of optimization-based approaches with respect to vehicle kinematics and dynamics, as well as actuator and spatial constraints. Copyright (C) 2022 The Authors.

关键词： Autonomous surface vehicles docking collision avoidance trajectory and path planning computational geometry optimal control theory

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A Mean Field Game Model of Spatial Evolutionary Games 21

A Mean Field Game Model of Spatial Evolutionary Games

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21st International conference on Autonomous Agents and Multiagent Systems, AAMAS 2022

作者： Hsiao, Vincent Nau, Dana University of Maryland College ParkMD United States

ISBN: (纸本)9781713854333

Evolutionary Game theory (EGT) studies evolving populations of agents that interact through normal form games whose outcome determines each individual's evolutionary fitness. In many applications, EGT models are extended to include spatial effects in which the agents are located in a structured population such as a graph. We propose a Mean Field Game (MFG) generalization, denoted Pair-MFG, of the spatial evolutionary game model such that the behavior of a given spatial evolutionary game (or more specifically the behavior of its pair approximation) is a special case trajectory of the corresponding MFG. The proposed Pair-MFG model also allows for the formulation of the spatial evolutionary game as a control problem, opening up additional avenues of research into controlling the outcomes of these games. The state evolution equations of the proposed model are highly nonlinear and none of the equations in the system are necessarily convex. This necessitates different numerical methods as compared to those for traditional linear Quadratic Gaussian MFGs. We provide a method for solving this new Pair-MFG model using fixed point iteration with time-dependent proximal terms and show empirically that this method is capable of finding a solution to a selection of EGT games. © 2022 International Foundation for Autonomous Agents and Multiagent Systems (***). All rights reserved

关键词： numerical methods

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Joint Task Partition and Computation Offloading for Latency-Sensitive Services in Mobile Edge Networks 18

Joint Task Partition and Computation Offloading for Latency-...

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18th IEEE International conference on Mobility, Sensing and Networking (MSN)

作者： Peng, Yujie Song, Xiaoqin Liu, Fang Xing, Guoliang Song, Tiecheng Southeast Univ Natl Mobile Commun Res Lab Nanjing Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing Peoples R China Chinese Univ Hong Kong Informat Engn Hong Kong Peoples R China Southeast Univ Shenzhen Res Inst Shenzhen Peoples R China

ISBN: (纸本)9781665464574

With the development of Internet of Things (IoT), wireless communication networks and Artificial Intelligence (AI), more and more real-time applications such as online games and autonomous driving have emerged. However, due to limited computing power and battery capacity, it has become increasingly difficult for local user devices to take on the full range of computing tasks under tight timing constraints. The emerging Mobile Edge Computing (MEC) technology is widely considered to be an important technology for achieving ultra-low latency. However, most of the existing work is focused on non-splittable computation tasks. In fact, data partitioning-oriented applications can be split into multiple subtasks for parallel processing. In this paper, we study the partial computation offloading of multiple detachable tasks in MEC networks, focusing on minimizing the total user device latency in the multi-MEC multiuser scenarios. Considering the dynamic partitioning of tasks, we adopt the barrel theory to construct a linear system of equations to find the optimal solutions and propose an approach for distributed computation offloading based on numerical methods. The simulation results show that the proposed algorithm can reduce the average user device latency by 31% compared with the binary offloading method.

关键词： MEC low-latency partial offloading numerical calculation method

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13th International conference on Optimization and applications, OPTIMA 2022

13th International Conference on Optimization and Applicatio...

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13th International conference on Optimization and applications, OPTIMA 2022

ISBN: (纸本)9783031225420

The proceedings contain 17 papers. The special focus in this conference is on Optimization and applications. The topics include: Application of the Interpolation Approach for Approximating Single-Machine Scheduling Problem with an Unknown Objective Function;robot Workspace Approximation with Modified Bicenetred Krawczyk Method;degenerate Equality Constrained Optimization Problems and P-Regularity theory;the Relative Formulation of the Quadratic Programming Problem in the Aircraft Assembly Modeling;an Accelerated Algorithm for Finding Efficient Solutions in Multiobjective Problems with Black-Box Multiextremal Criteria;the Best Ellipsoidal Estimates of Invariant Sets for a Third-Order Switched Affine System;prize-Collecting Asymmetric Traveling Salesman Problem Admits Polynomial Time Approximation Within a Constant Ratio;control of the Motion of Heating Sources of a Rod with Non-linear Feedback;terminal Control of Multi-agent System;qualitative Analysis of an Infinite Horizon Optimal Control Problem of a Shallow Lake;preface;decomposition Method for Solving the Quadratic Programming Problem in the Aircraft Assembly Modeling;some Adaptive First-Order methods for Variational Inequalities with Relatively Strongly Monotone Operators and Generalized Smoothness;compression and Data Similarity: Combination of Two Techniques for Communication-Efficient Solving of Distributed Variational Inequalities;numerical Analysis of the Model of Optimal Savings and Borrowing.

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Acceleration and restart for the randomized Bregman-Kaczmarz method

arXiv

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arXiv 2023年

作者： Tondji, Lionel Necoara, Ion Lorenz, Dirk A. Institute for Analysis and Algebra TU Braunschweig Braunschweig38092 Germany Center for Industrial Mathematics University of Bremen Postfach 330440 Bremen28334 Germany Automatic Control and Systems Engineering Department National University of Science and Technology Politehnica Bucharest Bucharest060042 Romania Gheorghe Mihoc-Caius Iacob Institute of Mathematical Statistics and Applied Mathematics The Romanian Academy Bucharest050711 Romania

Optimizing strongly convex functions subject to linear constraints is a fundamental problem with numerous applications. In this work, we propose a block (accelerated) randomized Bregman-Kaczmarz method that only uses a block of constraints in each iteration to tackle this problem. We consider a dual formulation of this problem in order to deal in an efficient way with the linear constraints. Using convex tools, we show that the corresponding dual function satisfies the Polyak-Lojasiewicz (PL) property, provided that the primal objective function is strongly convex and verifies additionally some other mild assumptions. However, adapting the existing theory on coordinate descent methods to our dual formulation can only give us sublinear convergence results in the dual space. In order to obtain convergence results in some criterion corresponding to the primal (original) problem, we transfer our algorithm to the primal space, which combined with the PL property allows us to get linear convergence rates. More specifically, we provide a theoretical analysis of the convergence of our proposed method under different assumptions on the objective and demonstrate in the numerical experiments its superior efficiency and speed up compared to existing methods for the same *** Codes 65F10, 68W20, 90C25 © 2023, CC BY.

关键词： linear systems

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Solving linear systems on a GPU with hierarchically off-diagonal low-rank approximations 22

Solving linear systems on a GPU with hierarchically off-diag...

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Proceedings of the International conference on High Performance Computing, Networking, Storage and Analysis

作者： Chao Chen Per-Gunnar Martinsson University of Texas at Austin

We are interested in solving linear systems arising from three applications: (1) kernel methods in machine learning, (2) discretization of boundary integral equations from mathematical physics, and (3) Schur complements formed in the factorization of many large sparse matrices. The coefficient matrices are often data-sparse in the sense that their off-diagonal blocks have low numerical ranks; specifically, we focus on "hierarchically off-diagonal low-rank (HODLR)" matrices. We introduce algorithms for factorizing HODLR matrices and for applying the factorizations on a GPU. The algorithms leverage the efficiency of batched dense linear algebra, and they scale nearly linearly with the matrix size when the numerical ranks are fixed. The accuracy of the HODLR-matrix approximation is a tunable parameter, so we can construct high-accuracy fast direct solvers or low-accuracy robust preconditioners. numerical results show that we can solve problems with several millions of unknowns in a couple of seconds on a single GPU.

关键词： elliptic partial differential equations LU factorization hierarchical matrix boundary integral equation hierarchical low-rank approximation rank structured matrix linear solver on GPU batched dense linear algebra kernel matrix

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Constructive Analysis of Eigenvalue Problems in Control under numerical Uncertainty

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2020年第9期18卷 2177-2185页

作者： Osinenko, Pavel Devadze, Grigory Streif, Stefan Tech Univ Chemnitz Automat Control & Syst Dynam Lab Reichenhainer Str 70 D-09126 Chemnitz Germany

The eigenvalue problem plays a central role in linear algebra and its applications in control and optimization methods. In particular, many matrix decompositions rely upon computation of eigenvalue-eigenvector pairs, such as diagonal or Jordan normal forms. Perturbation theory and various regularization techniques help address some numerical difficulties of computation eigenvectors, but often rely on per se uncomputable quantities, such as a minimal gap between eigenvalues. In this note, the eigenvalue problem is revisited within constructive analysis allowing to explicitly consider numerical uncertainty. Exact eigenvectors are substituted by approximate ones in a suitable format. Examples showing influence of computation precision are provided.

关键词： Approximate solutions constructive analysis eigenvalues eigenvectors fundamental theorem of algebra

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Regularization of Feynman 4-Loop Integrals with numerical Integration and Extrapolation 22nd

Regularization of Feynman 4-Loop Integrals with Numerical ...

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22nd International conference on Computational Science and Its applications , ICCSA 2022

作者： de Doncker, E. Yuasa, F. Western Michigan University KalamazooMI49008 United States 1-1 OHO Tsukuba Ibaraki305-0801 Japan

ISBN: (纸本)9783031105616

In this paper we continue our recent work on evaluating numerical approximations for a set of 4-loop self-energy integrals required in the computation of higher orders in perturbation theory. The results are given by a Laurent expansion in the dimensional regularization parameter, Ε, where Ε is related to the space-time dimension as ν= 4 - 2 Ε. Although the leading-order coefficients for the diagrams with massless internal lines are given in analytic form in the literature, we obtain them using a numerical approach and with modern computational techniques. In a similar manner, we derive results for diagrams with massive lines. The SIMD (Single Instruction, Multiple Data) nature of the computation of loop integrals based on composite lattice rules lends itself to an efficient GPU implementation. We further apply double exponential numerical integration layered over the message passing interface (MPI) parallel platform. Limits of integral sequences (as the regularization parameter tends to zero) are implemented numerically using linear and nonlinear extrapolation procedures. numerical results are given to illustrate the versatility of the methods and show some robustness with regard to the selection of sequence parameters. © 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.

关键词： Message passing

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A Low-Rank Approach for Nonlinear Parameter-Dependent Fluid-Structure Interaction Problems

A Low-Rank Approach for Nonlinear Parameter-Dependent Fluid-...

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European conference on numerical Mathematics and Advanced applications, ENUMATH 2019

作者： Benner, Peter Richter, Thomas Weinhandl, Roman Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany Otto von Guericke University Magdeburg Magdeburg Germany

ISBN: (纸本)9783030558734

Parameter-dependent discretizations of linear fluid-structure interaction problems can be approached with low-rank methods. When discretizing with respect to a set of parameters, the resulting equations can be translated to a matrix equation since all operators involved are linear. If nonlinear fluid-structure interaction problems are considered, a direct translation to a matrix equation is not possible. We present a method that splits the parameter set into disjoint subsets and, on each subset, computes an approximation of the problem related to the upper median parameter by means of the Newton iteration. This approximation is then used as initial guess for one Newton step on a subset of problems. © 2021, Springer Nature Switzerland AG.

关键词： Matrix algebra

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Towards Scalable Automatic Exploration of Bifurcation Diagrams for Large-Scale applications

Towards Scalable Automatic Exploration of Bifurcation Diagra...

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European conference on numerical Mathematics and Advanced applications, ENUMATH 2019

作者： Thies, Jonas Wouters, Michiel Hennig, Rebekka-Sarah Vanroose, Wim German Aerospace Center Cologne Germany University of Antwerp Antwerp Belgium

ISBN: (纸本)9783030558734

The Trilinos library LOCA (http://***/LOCA/ ) allows computing branches of steady states of large-scale dynamical systems like (discretized) nonlinear PDEs. The core algorithms typically are (pseudo-)arclength continuation, Newton–Krylov methods and (sparse) eigenvalue solvers. While LOCA includes some basic techniques for computing bifurcation points and switching branches, the exploration of a complete bifurcation diagram still takes a lot of programming effort and manual interference. On the other hand, recent developments in algorithms for fully automatic exploration are condensed in PyNCT (https://***/project/PyNCT/ ). The scope of this algorithmically versatile software is, however, limited to relatively small (e.g. 2D) problems because it relies on linear algebra from Python libraries like NumPy. Furthermore, PyNCT currently does not support problems with a non-Hermitian Jacobian matrix, which rules out interesting applications in chemistry and fluid dynamics. In this paper we aim to combine the best of both worlds: a high-level implementation of algorithms in PyNCT with parallel models and linear algebra implemented in Trilinos. PyNCT is extended to non-symmetric systems and its complete backend is replaced by the PHIST library (https://***/essex/phist ), which allows us to use the same underlying HPC libraries as LOCA does. We then apply the new code to a reaction-diffusion model to demonstrate its potential of enabling fully automatic bifurcation analysis on parallel computers. © 2021, Springer Nature Switzerland AG.

关键词： Jacobian matrices

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