This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such a...
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This paper develops a novel limited-memory method to solve dynamic optimization problems. The memory requirements for such problems often present a major obstacle, particularly for problems with PDE constraints such as optimal flow control, full waveform inversion, and optical tomography. In these problems, PDE constraints uniquely determine the state of a physical system for a given control;the goal is to find the value of the control that minimizes an objective. While the control is often low dimensional, the state is typically more expensive to store. This paper suggests using randomized matrix approximation to compress the state as it is generated and shows how to use the compressed state to reliably solve the original dynamic optimization problem. Concretely, the compressed state is used to compute approximate gradients and to apply the Hessian to vectors. The approximation error in these quantities is controlled by the target rank of the sketch. This approximate first- and second-order information can readily be used in any optimization algorithm. As an example, we develop a sketched trust-region method that adaptively chooses the target rank using a posteriori error information and provably converges to a stationary point of the original problem. Numerical experiments with the sketched trust-region method show promising performance on challenging problems such as the optimal control of an advection-reaction-diffusion equation and the optimal control of fluid flow past a cylinder.
Electric vehicle charging stations (EVCSs) come along with great challenges for the power grid due to their highly uncertain load characteristic. This is particularly the case for charging stations located in nonresid...
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Electric vehicle charging stations (EVCSs) come along with great challenges for the power grid due to their highly uncertain load characteristic. This is particularly the case for charging stations located in nonresidential areas, such as commercial centers, company sites, or car-rental stations. For a safe and sustainable operation of the power grid, distribution system operators require reliable load forecasts of such charging stations. In this brief, a robust EVCS management strategy is proposed, which provides a day-ahead upper limit profile of the EVCS's power consumption. In real time, this upper limit profile is strictly respected while guaranteeing-at a configurable probability-the Quality of Service. The strategy is based on randomized algorithms and relies on a statistic occupancy model of the EVCS while not requiring any online forecasts of each EVs' arrival and departure schedules. In a case study based on statistic data, which has been provided by the Euref Campus in Berlin, the feasibility and relevance of the proposed approach are demonstrated.
This paper presents an adaptive randomized algorithm for computing the butterfly factorization of an m x n matrix with m ti n provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors...
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This paper presents an adaptive randomized algorithm for computing the butterfly factorization of an m x n matrix with m ti n provided that both the matrix and its transpose can be rapidly applied to arbitrary vectors. The resulting factorization is composed of O(logn) sparse factors, each containing O(n) nonzero entries. The factorization can be attained using O(n(3/2) logn) computation and O(n logn) memory resources. The proposed algorithm can be implemented in parallel and can apply to matrices with strong or weak admissibility conditions arising from surface integral equation solvers as well as multi-frontal-based finite-difference, finite-element, or finite-volume solvers. A distributed-memory parallel implementation of the algorithm demonstrates excellent scaling behavior.
In this paper we propose a Simulated Annealing (SA) based energy-efficient task scheduling algorithm for multi-core processors, the Simulated Annealing Energy Efficient Task Scheduling algorithm (SAEETSA), and compare...
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ISBN:
(纸本)9789897585340
In this paper we propose a Simulated Annealing (SA) based energy-efficient task scheduling algorithm for multi-core processors, the Simulated Annealing Energy Efficient Task Scheduling algorithm (SAEETSA), and compare it with another algorithm, the Energy Efficient Task Scheduling algorithm (EETSA). Our results show that for dual-core processors the SAEETSA algorithm is taking up to 16.78% less energy as compared to the EETSA algorithm, and for tri-core processors, the SAEETSA algorithm is taking up to 26.97% less energy as compared to the EETSA algorithm.
randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-c...
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randomized algorithms for low-rank matrix approximation are investigated, with the emphasis on the fixed-precision problem and computational efficiency for handling large matrices. The algorithms are based on the so-called QB factorization, where Q is an orthonormal matrix. First, a mechanism for calculating the approximation error in the Frobenius norm is proposed, which enables efficient adaptive rank determination for a large and/or sparse matrix. It can be combined with any QB-form factorization algorithm in which B's rows are incrementally generated. Based on the blocked randQB algorithm by Martinsson and Voronin, this results in an algorithm called randQB_EI. Then, we further revise the algorithm to obtain a pass-efficient algorithm, randQB_FP, which is mathematically equivalent to the existing randQB algorithms and also suitable for the fixed-precision problem. Especially, randQB_FP can serve as a single-pass algorithm for calculating leading singular values, under a certain condition. With large and/or sparse test matrices, we have empirically validated the merits of the proposed techniques, which exhibit remarkable speedup and memory saving over the blocked randQB algorithm. We have also demonstrated that the single-pass algorithm derived by randQB_FP is much more accurate than an existing single-pass algorithm. And with data from a scenic image and an information retrieval application, we have shown the advantages of the proposed algorithms over the adaptive range finder algorithm for solving the fixed-precision problem.
Regularization is possibly the most popular method for solving discrete ill-posed prob-lems, whose solution is less sensitive to the error in the observed vector in the right hand than the original solution. This pape...
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Regularization is possibly the most popular method for solving discrete ill-posed prob-lems, whose solution is less sensitive to the error in the observed vector in the right hand than the original solution. This paper presents a new modified truncated randomized singular value decomposition (TR-MTRSVD) method for large Tikhonov regularization in standard form. The proposed TR-MTRSVD algorithm introduces the idea of randomized algorithm into the improved truncated singular value decomposition (MTSVD) method to solve large Tikhonov regularization problems. The approximation matrix A & SIM;l produced by randomized SVD is replaced by the closest matrix A & SIM;k & SIM;in a unitarily invariant matrix norm with the same spectral condition number. The regularization parameters are determined by the discrepancy principle. Numerical examples show the effectiveness and efficiency of the proposed TR-MTRSVD algorithm for large Tikhonov regularization problems. (C) 2021 Elsevier B.V. All rights reserved.
In order to describe or estimate different quantities related to a specific random variable, it is of prime interest to numerically generate such a variate. In specific situations, the exact generation of random varia...
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In order to describe or estimate different quantities related to a specific random variable, it is of prime interest to numerically generate such a variate. In specific situations, the exact generation of random variables might be either momentarily unavailable or too expensive in terms of computation time. It therefore needs to be replaced by an approximation procedure. As was previously the case, the ambitious exact simulation of first exit times for diffusion processes was unreachable though it concerns many applications in different fields like mathematical finance, neuroscience or reliability. The usual way to describe first exit times was to use discretization schemes, that are of course approximation procedures. Recently, Herrmann and Zucca (Herrmann and Zucca, 2020) proposed a new algorithm, the so-called GDET-algorithm (General Diffusion Exit Time), which permits to simulate exactly the first exit time for one-dimensional diffusions. The only drawback of exact simulation methods using an acceptance-rejection sampling is their time consumption. In this paper the authors highlight an acceleration procedure for the GDET-algorithm based on a multi-armed bandit model. The efficiency of this acceleration is pointed out through numerical examples.
We investigate the complex optimization problem that arises in the planning of the transition process from traditional public transport to electric transport. We define the assumptions, input and output parameters of ...
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We investigate the complex optimization problem that arises in the planning of the transition process from traditional public transport to electric transport. We define the assumptions, input and output parameters of the problem, as well as its mathematical model and a randomized algorithm for solving it. We also give an extensive bibliography of publications on the problem at hand.
This paper focuses on studying the message complexity of implicit leader election in synchronous distributed networks of diameter two. Kutten et al. (J ACM 62(1):7:1-7:27, 2015) showed a fundamental lower bound of Ome...
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This paper focuses on studying the message complexity of implicit leader election in synchronous distributed networks of diameter two. Kutten et al. (J ACM 62(1):7:1-7:27, 2015) showed a fundamental lower bound of Omega(m) (m is the number of edges in the network) on the message complexity of (implicit) leader election that applied also to Monte Carlo randomized algorithms with constant success probability;this lower bound applies for graphs that have diameter at least three. On the other hand, for complete graphs (i.e., graphs with diameter one), Kutten et al. (Theor Comput Sci 561(Part B):134-143, 2015) established a tight bound of (Theta) over tilde(root n) on the message complexity of randomized leader election (n is the number of nodes in the network). For graphs of diameter two, the complexity was not known. In this paper, we settle this complexity by showing a tight bound of (Theta) over tilde (n) on the message complexity of leader election in diameter-two networks. We first give a simple randomized Monte-Carlo leader election algorithm that with high probability (i.e., probability at least 1 - n(-c), for some fixed positive constant c) succeeds and uses O(n log(3) n) messages and runs in O(1) rounds;this algorithm works without knowledge of n (and hence needs no global knowledge). We then show that any algorithm (even Monte Carlo randomized algorithms with large enough constant success probability) needs O(n) messages (even when n is known), regardless of the number of rounds. We also present an O(n log n) message deterministic algorithm that takes O(log n) rounds (but needs knowledge of n);we show that this message complexity is tight for deterministic algorithms. Together with the two previous results of Kutten et al., our results fully characterize the message complexity of leader election vis-a-vis the graph diameter.
This paper presents an improved randomized Circle Detection (RCD) algorithm with the characteristic of circularity to detect randomized circle in images with complex background, which is not based on the Hough Transfo...
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This paper presents an improved randomized Circle Detection (RCD) algorithm with the characteristic of circularity to detect randomized circle in images with complex background, which is not based on the Hough Transform. The experimental results denote that this algorithm can locate the circular mark of Printed Circuit Board (PCB).
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