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作者： Lee, Kooktae Texas A&M University

学位级别：Ph.D.

This dissertation addresses research problems related to the switched system as well as its application to large-scale asynchronous dynamical systems. For decades, this switched system has been widely studied in depth, owing to the broad applicability of the switched system framework. For example, the switched system can be adopted for modeling the dynamics of numerous systems including power systems, manufacturing systems, aerospace systems, networked control systems, etc. Despite considerable research works that have been developed during last several decades, there are still remaining yet important and unsolved problems for the switched systems. In the first part of this dissertation, new methods are developed for uncertainty propagation of stochastic switched systems in the presence of the state uncertainty, represented by probability density functions(PDFs). The main difficulty of this problem is that the number of PDF components in the state increases exponentially under the stochastic switching, incurring the curse of dimensionality. This dissertation provides a novel method that circumvents the issue regarding the curse of dimensionality. As an extension of this research, the new method for the switching synthesis is presented in the second part, to achieve the optimal performance of the switched system. This research is relevant to developing the switching synthesis on how to switch between different switching modes. In the following chapters, some interesting applications that emerges as today's leading-edge technology in high-performance computing (HPC) will be introduced. Generally, the massive parallel computing entails idle process time in multi-core processors or distributed computing devices as up to 80% of total computation time, owing to the synchronization of the data. Thus, there is a trend toward relaxing such a restriction on synchronization penalty to overcome this bottleneck problem. This dissertation presents a synchronous computing algorith

关键词： switched system analysis and synthesis asynchronous algorithm distributed quadratic programming large-scale networked control system Thesis

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Parallel asynchronous Stochastic Dual Coordinate Descent algorithms for High Efficiency and Stable Convergence

Parallel Asynchronous Stochastic Dual Coordinate Descent Alg...

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29th Euromicro International Conference on Parallel, Distributed and Network-Based Processing (PDP)

作者： Chen, Yung-Chen Liu, Pangfeng Wu, Jan-Jan Natl Taiwan Univ Dept Comp Sci & Informat Engn Taipei Taiwan Natl Taiwan Univ Grad Inst Networking & Multimedia Taipei Taiwan Acad Sinica Inst Informat Sci Taipei Taiwan

ISBN: (纸本)9781665414555

Parallel asynchronous stochastic dual coordinate descent algorithm (PASSCoDe) is an efficient method to train linear models in multi-core shared-memory systems. PASSCoDe enjoys a good speedup when the number of threads is less than 8 on sparse datasets, i.e., the percentage of nonzero elements in the training data is relatively small. However, due to the memory conflict and delayed parameter access problem in parallel execution, it often diverges or does not converge to the best accuracy as a serial dual coordinate descent algorithm does. In this paper, we propose two algorithms - Adaptive Hybrid algorithm and Lazy-Sync algorithm, to overcome the convergence issues in parallel execution. Both algorithms use the current accuracy to guide the execution and strike a balance between accuracy and efficiency. Experimental results indicate that both algorithms converge to the same high accuracy as a sequential program does on all datasets tested except on an extremely small one. On the other hand, PASSCoDe sometimes converges to a less accurate value or does not converge at all on some datasets. Our methods also outperform PASSCoDe-Fix, an improved version of PASSCoDe, in stable convergence, execution speed, and scalability. For example, the Adaptive llybrid algorithm runs up to 2.8 times faster than PASSCoDe-Fix, and the Lazy-Sync algorithm runs 11 times faster than PASSCoDe-Fix on dataset covt ype with 10 threads.

关键词： Machine learning parallel dual coordinate descent asynchronous algorithm linear model support vector machine

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Decentralized Dual Operator Splitting for Nonsmooth Composite Optimization

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IEEE TRANSACTIONS ON NETWORK SCIENCE AND ENGINEERING 2022年第4期9卷 2084-2097页

作者： Li, Huaqing Ding, Wentao Wang, Zheng Lu, Qingguo Li, Yongfu Xia, Dawen Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligen Coll Elect & Informat Engn Chongqing 400715 Peoples R China Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Chongqing Univ Coll Comp Sci Chongqing 400044 Peoples R China Chongqing Univ Posts & Telecommun Key Lab Intelligent Air Ground Cooperat Control U Coll Automat Chongqing 400065 Peoples R China Guizhou Minzu Univ Coll Data Sci & Informat Engn Guiyang 550025 Peoples R China

Inspired by the advantages of the decentralized network structure in large-scale data processing and system robustness, this paper considers a fully distributed computation strategy for a nonsmooth composite optimization problem. The goal is to solve the problem only by resorting to local computation and local communications. Here, the local objective function is composed of two possibly nonsmooth functions where one is strongly convex and the other is proper closed convex (not necessarily strongly convex). Through associating variables with the agents and edges of the network, a decentralized synchronous algorithm is developed based on the dual operator splitting method. The asynchronous version of the proposed algorithm is further developed based on the randomized block coordinate descent technique, where each agent performs the algorithm only under its independent activation. Then the convergence analysis is provided depending on the fixed point iterations and the property of strong duality. Simulations on regularized problems demonstrate the effectiveness of the proposed decentralized algorithm.

关键词： Signal processing algorithms Linear programming Cost function Convex functions Symmetric matrices Signal processing Resource management Decentralized optimization multi-agent system nonsmooth problem asynchronous algorithm randomized block coordinate uncoordinated stepsize

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Study of asynchronicity in the fluid-structure interaction domain

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2021年 93卷 156-167页

作者： Ramirez, C. Leroyer, A. Visonneau, M. Roux, Y. Cent Nantes LHEEA UMR CNRS 6598 1 Rue Noe F-44321 Nantes 3 France K Epsilon 1300 Route Cretes F-06560 Valbonne France

With the objective of studying fluid-structure interaction (FSI) applications with sophisticated structural behavior, this work studies an approach that makes room for the use of complex structural models without penalizing the global computational time. The proposed approach is based on an algorithm that, simultaneously solving two subdomains, allows an asynchronous update of the boundary conditions at the interface according to the computational time spent by each of the solvers. The implementation of this algorithm revealed the appearance of numerical instabilities related to the parallel operation, and the independent evolution of the local solution in each subdomain. To overcome these stability problems, this work proposes a two-part stabilization strategy, both based on the use of a modal approach, as well as the adjustment of the formulation of the Jacobian of the fluid at the interface. The first part consists of a predictor-corrector method for the parallel operation and the second in an auxiliary coupling to assist the solution of the fluid domain. The impact of parameters such as the amount of correction, the number of modes and under-relaxation are studied. The use of the proposed asynchronous algorithm shows a positive impact when used for the solution of weakly coupled FSI applications (mass ratio m(F)/m(S) = 0.001). However, for applications with a larger or equivalent mass ratio, m(F)/m(S) = 0.1or m(F)/m(S) = 1, greater difficulty in stabilizing remain. Even though it is found that the proposed approach requires to be improved to ensure a robust solution, the encountered results represent an advance towards the use of an innovative algorithm in the FSI domain, one that could naturally offer an intermediary algorithm between the implicit external algorithm and the implicit internal algorithm.

关键词： FSI asynchronous algorithm Numerical stabilization Strong couplings RANS CFD Non-linear FEM

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Distributed Primal-Dual Splitting algorithm for Multiblock Separable Optimization Problems

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 2022年第8期67卷 4264-4271页

作者： Li, Huaqing Wu, Xiangzhao Wang, Zheng Huang, Tingwen Southwest Univ Chongqing Key Lab Nonlinear Circuits & Intelligen Coll Elect & Informat Engn Chongqing 400715 Peoples R China Univ New South Wales Sch Elect Engn & Telecommun Sydney NSW 2052 Australia Texas A&M Univ Sci Program Doha 23874 Qatar

This article considers the distributed structured optimization problem of collaboratively minimizing the global objective function composed of the sum of local cost functions. Each local objective function involves a Lipschitz-differentiable convex function, a nonsmooth convex function, and a linear composite nonsmooth convex function. For such problems, we derive the synchronous distributed primal-dual splitting (S-DPDS) algorithm with uncoordinated stepsizes. Meanwhile, we develop the asynchronous version of the algorithm in light of the randomized block-coordinate method (A-DPDS). Further, the convergence results show the relaxed range and concise form of the acceptable parameters, which indicates that the algorithms are conducive to the selection of parameters in practical applications. Finally, we demonstrate the efficiency of S-DPDS and A-DPDS algorithms by numerical experiments.

关键词： Optimization Convex functions Distributed algorithms Convergence Linear programming Couplings Simulation asynchronous algorithm distributed optimization primal-dual splitting algorithm uncoordinated stepsizes

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A distributed simplex algorithm for degenerate linear programs and multi-agent assignments

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AUTOMATICA 2012年第9期48卷 2298-2304页

作者： Buerger, Mathias Notarstefano, Giuseppe Bullo, Francesco Allgoewer, Frank Univ Stuttgart Inst Syst Theory & Automat Control D-70550 Stuttgart Germany Univ Lecce Dept Engn I-73100 Lecce Italy Univ Calif Santa Barbara Ctr Control Dynam Syst & Computat Santa Barbara CA 93106 USA

In this paper we propose a novel distributed algorithm to solve degenerate linear programs on asynchronous peer-to-peer networks with distributed information structures. We propose a distributed version of the well-known simplex algorithm for general degenerate linear programs. A network of agents, running our algorithm, will agree on a common optimal solution, even if the optimal solution is not unique, or will determine infeasibility or unboundedness of the problem. We establish how the multi-agent assignment problem can be efficiently solved by means of our distributed simplex algorithm. We provide simulations supporting the conjecture that the completion time scales linearly with the diameter of the communication graph. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Distributed simplex Distributed linear programming asynchronous algorithm Multi-agent task assignment

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Multivariate Monotone Inclusions in Saddle Form

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MATHEMATICS OF OPERATIONS RESEARCH 2022年第2期47卷 1082-1109页

作者： Bui, Minh N. Combettes, Patrick L. North Carolina State Univ Dept Math Raleigh NC 27695 USA

We propose a novel approach to monotone operator splitting based on the notion of a saddle operator. Under investigation is a highly structured multivariate monotone inclusion problem involving a mix of set-valued, cocoercive, and Lipschitzian monotone operators, as well as various monotonicity-preserving operations among them. This model encompasses most formulations found in the literature. A limitation of existing primal-dual algorithms is that they operate in a product space that is too small to achieve full splitting of our problem in the sense that each operator is used individually. To circumvent this difficulty, we recast the problem as that of finding a zero of a saddle operator that acts on a bigger space. This leads to an algorithm of unprecedented flexibility, which achieves full splitting, exploits the specific attributes of each operator, is asynchronous, and requires to activate only blocks of operators at each iteration, as opposed to activating all of them. The latter feature is of critical importance in large-scale problems. The weak convergence of the main algorithm is established, aswell as the strong convergence of a variant. Various applications are discussed, and instantiations of the proposed framework in the context of variational inequalities and minimization problems are presented.

关键词： monotone inclusion monotone operator saddle form operator splitting block-iterative algorithm asynchronous algorithm strong convergence

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Optimization flow control - I: Basic algorithm and convergence

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IEEE-ACM TRANSACTIONS ON NETWORKING 1999年第6期7卷 861-874页

作者： Low, SH Lapsley, DE Univ Melbourne Dept Elect & Elect Engn Parkville Vic 3052 Australia

We propose an optimization approach to flow control where the objective is to maximize the aggregate source utility over their transmission rates. We view network links and sources as processors of a distributed computation system to solve the dual problem using a gradient projection algorithm;In this system, sources select transmission rates that maximize their own benefits, utility minus bandwidth cost, and network links adjust bandwidth prices to coordinate the sources' decisions. We allow feedback delays to be different, substantial, and time varying, and links and sources to update at different times and with different frequencies, We provide asynchronous distributed algorithms and prove their convergence in a static environment. We present measurements obtained from a preliminary prototype to illustrate the convergence of the algorithm in a slowly time-varying environment. We discuss its fairness property.

关键词： asynchronous algorithm congestion pricing convergence gradient projection optimization flow control

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Relaxed approach for the parallel solution of security-constrained dispatch with post-contingency rescheduling

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IEE PROCEEDINGS-GENERATION TRANSMISSION AND DISTRIBUTION 2003年第3期150卷 291-296页

作者： Saavedra, OR Univ Fed Maranhao Dept Elect Engn Grp Sistemas Protencia Sao Luis MA Brazil

Some approaches for the solution of the security-constrained dispatch with postcontingency corrective rescheduling problem in a multiprocessing environment are presented. These approaches can be interpreted as relaxed versions of the classical Benders decomposition. The idea is to improve the computational efficiency when the problem is solved by using parallel processing. Results from one of these approaches implemented into an asynchronous algorithm are reported here. Some strategies for improving performance are discussed and test results with two real-life Brazilian systems are reported.

关键词： power system security Power engineering computing post-contingency rescheduling Benders decomposition Multiprocessing systems Generating stations and plants parallel processing multiprocessing environment real-life Brazilian systems Security aspects parallel solution power generation dispatch power system analysis computing Power system management, operation and economics asynchronous algorithm security-constrained dispatch power generation scheduling computational efficiency Power system control

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From adaptive renaming to set agreement

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THEORETICAL COMPUTER SCIENCE 2009年第14期410卷 1328-1335页

作者： Gafni, Eli Mostefaoui, Achour Raynal, Michel TraverS, Corentin IRISA F-35042 Rennes France Univ Calif Los Angeles Dept Comp Sci Los Angeles CA 90095 USA

The adaptive M-renaming problem consists of providing processes with a new name taken from a name space whose size M depends only oil the number p of processes that participate in the renaming (and not oil the total number n of processes that could ask for a new name). The k-set agreement problem allows each process that proposes a value to decide a proposed Value in such a way that at most k different values are decided. In an asynchronous system prone to up to t process crash failures. and where processes can cooperate by accessing atomic read/write registers only, the best that can be done is a renaming space of size M = p + t. In the same setting, the k-set agreement problem cannot be solved when t >= k. This paper focuses oil the way a solution to the adaptive renaming problem can help in solving the k-set agreement problem when t >= k. It has two contributions. Considering the case k = t (1 <= t < n). the first contribution is a t-resilient algorithm that solves the k-set agreement problem from any adaptive (p + k - 1)-renaming algorithm. The second contribution considers the case k < t. It shows that there is no such wait-free algorithm when k < n/2 (wait-free means t = n - 1). So, while a solution to the adaptive (,p + k - 1)renaming problem allows t-resiliently solving the k-set agreement problem despite t = k failures, when k < t such an additional power becomes useless for the values of n > 2k (i.e. adaptive (p + k - 1)-renaming allows progressing from k > t to k = t, but does not allow bypassing the "k = t" frontier when n > 2k). (C) 2008 Elsevier B.V. All rights reserved.

关键词： Adaptive renaming asynchronous algorithm Atomic register Atomic snapshot Participating process Reduction Set agreement Shared object t-resilient algorithm Wait-free algorithm

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