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Speeding up stochastic reconstructions of binary images from limited projection directions

LINEAR ALGEBRA AND ITS APPLICATIONS 2001年第1-3期339卷 75-89页

作者： Vardi, E Herman, GT Kong, TY Univ Penn Med Ctr MR Learning Ctr Dept Bioengn Philadelphia PA 19104 USA CUNY Grad Ctr Dept Comp Sci New York NY 10016 USA CUNY Queens Coll Dept Comp Sci Flushing NY 11367 USA Univ Penn Dept Radiol Med Image Proc Grp Philadelphia PA 19104 USA Temple Univ Ctr Comp Sci & Appl Math Philadelphia PA 19122 USA Temple Univ Dept Comp & Informat Sci Philadelphia PA 19122 USA

In earlier work, a stochastic method for reconstructing certain classes of two-dimensional binary images from limited projection directions was presented. In the present study, we experiment with different implementations of this method to minimize the running time. Our fastest implementation is based on a took-up table and pre-generated arrays of random integers. This is more than 40 times faster than the implementation used in the earlier work. This speedup makes it practical to conduct extensive searches to find the optimal values of the method's parameters for each class of images to be reconstructed. (C) 2001 Elsevier Science Inc. All rights reserved.

关键词： image reconstruction binary tomography stochastic algorithm computer time look-up table

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stochastic incremental mirror descent algorithms with Nesterov smoothing

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NUMERICAL algorithmS 2024年第1期95卷 351-382页

作者： Bitterlich, Sandy Grad, Sorin-Mihai Tech Univ Chemnitz Fac Math D-09126 Chemnitz Germany Inst Polytech Paris Unite Math Appl ENSTA Paris F-91120 Palaiseau France

For minimizing a sum of finitely many proper, convex and lower semicontinuous functions over a nonempty closed convex set in an Euclidean space we propose a stochastic incremental mirror descent algorithm constructed by means of the Nesterov smoothing. Further, we modify the algorithm in order to minimize over a nonempty closed convex set in an Euclidean space a sum of finitely many proper, convex and lower semicontinuous functions composed with linear operators. Next, a stochastic incremental mirror descent Bregman-proximal scheme with Nesterov smoothing is proposed in order to minimize over a nonempty closed convex set in an Euclidean space a sum of finitely many proper, convex and lower semicontinuous functions and a prox-friendly proper, convex and lower semicontinuous function. Different to the previous contributions from the literature on mirror descent methods for minimizing sums of functions, we do not require these to be (Lipschitz) continuous or differentiable. Applications in Logistics, Tomography and Machine Learning modelled as optimization problems illustrate the theoretical achievements

关键词： Mirror descent method stochastic algorithm Nesterov smoothing Incremental algorithm Proximal point algorithm PET image reconstructions Location problem

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The compact law of the iterated logarithm for multivariate stochastic approximation algorithms

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stochastic ANALYSIS AND APPLICATIONS 2005年第1期23卷 181-203页

作者： Mokkadem, A Pelletier, M Univ Versailles St Quentin Dept Math F-78035 Versailles France

We consider a sequence (Z(n))(ngreater than or equal to1) defined by a general multivariate stochastic approximation algorithm and assume that (Z(n)) converges to a solution z* almost surely. We establish the compact law of the iterated logarithm for Z(n) by proving that, with probability one, the limit set of the sequence (Z(n) - z*) suitably normalized is an ellipsoid. We also give the law of the iterated logarithm for the l(P) norms, p is an element of [1, infinity], of (Z(n) - z*).

关键词： law of the iterated logarithm stochastic algorithm

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Simultaneous perturbation stochastic approximation: towards one-measurement per iteration

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NUMERICAL algorithmS 2023年第3期94卷 1085-1101页

作者： Li, Shiru Xia, Yong Xu, Zi Beihang Univ Sch Math Sci Beijing 100191 Peoples R China Shanghai Univ Dept Math Shanghai 200444 Peoples R China

When measuring the value of a function to be minimized is not only expensive but also with noise, the popular simultaneous perturbation stochastic approximation (SPSA) algorithm requires only two function values in each iteration. In this paper, we present a method requiring only one function measurement value per iteration in the average sense. We prove the strong convergence and asymptotic normality of the new algorithm. Limited experimental results demonstrate the effectiveness and potential of our algorithm for solving low-dimensional problems.

关键词： Unconstrained optimization stochastic algorithm Approximating gradient SPSA

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stochastic-Based Optimization Strategy of Dimethyl Oxalate Hydrogenation for Ethylene Glycol Production

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PROCESS INTEGRATION AND OPTIMIZATION FOR SUSTAINABILITY 2024年第4期8卷 1149-1162页

作者： Rohman, Fakhrony Sholahudin Alwi, Sharifah Rafidah Wan Kelani, Rasheed Olakunle Muhammad, Dinie Azmi, Ashraf Murat, Muhamad Nazri Univ Teknol Malaysia Res Inst Sustainable Environm RISE Proc Syst Engn Ctr PROSPECT Bahru 81310 Johor Malaysia Univ Teknol Malaysia Fac Chem & Energy Engn Dept Chem Engn Skudai 81310 Johor Malaysia Univ Sains Malaysia Sch Chem Engn Engn CampusSeri AmpanganNibong Tebal Perai 14300 Penang Malaysia Univ Teknol MARA Coll Engn Sch Chem Engn Selangor 40450 Shah Alam Malaysia

The multi-objective optimization (MOO) of ethylene glycol (EG) production in a hydrogenation tubular reactor focuses on two main objectives: increasing yield and reducing energy cost. A model-based optimization approach using the ASPEN Plus simulator was employed to simulate the reactions. In addition, an inequality constraint was imposed on the reactor temperature to prevent a runaway condition. To solve the optimization problems, three multi-objective stochastic optimization algorithms, which are the multi-objective stochastic paint optimizer (MOSPO), multi-objective slime mold algorithm (MOSMA), and multi-objective dragonfly algorithm (MODA), were utilized along with MATLAB and ASPEN Plus simulator. In addition, performance metrics including hypervolume (H), pure diversity (PD), and spacing (S) were employed to evaluate and decide the most effective MOO approach. The results show that the most effective MOO approach for EG production in a hydrogenation tubular reactor is MODA. Its solution set provides precise, diverse, and well-distributed allocation of ND points along the Pareto Front (PF). Also, the results indicate that the highest productivity, lowest energy cost, and highest yield achieved are RM41.3499 million/year, RM0.1667 million/year, and 95.5249%, respectively. Furthermore, the plots of decision variables demonstrate that the reactor pressure highly impacts the optimal solution.

关键词： Multi-objective optimization Tubular reactors Hydrogenation stochastic algorithm Pareto front

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stochastic FORWARD-BACKWARD AND PRIMAL-DUAL APPROXIMATION algorithmS WITH APPLICATION TO ONLINE IMAGE RESTORATION 24

STOCHASTIC FORWARD-BACKWARD AND PRIMAL-DUAL APPROXIMATION AL...

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24th European Signal Processing Conference (EUSIPCO)

作者： Combettes, Patrick L. Pesquet, Jean-Christophe UPMC Univ Paris 06 Sorbonne Univ Lab Jacques Louis Lions UMR 7598 Paris France Univ Paris Est Lab Informat Gaspard Monge CNRS UMR 8049 Champs Sur Marne France

ISBN: (纸本)9780992862657

stochastic approximation techniques have been used in various contexts in data science. We propose a stochastic version of the forward-backward algorithm for minimizing the sum of two convex functions, one of which is not necessarily smooth. Our framework can handle stochastic approximations of the gradient of the smooth function and allows for stochastic errors in the evaluation of the proximity operator of the nonsmooth function. The almost sure convergence of the iterates generated by the algorithm to a minimizer is established under relatively mild assumptions. We also propose a stochastic version of a popular primal-dual proximal splitting algorithm, establish its convergence, and apply it to an online image restoration problem.

关键词： convex optimization nonsmooth optimization primal-dual algorithm stochastic algorithm parallel algorithm proximity operator recovery image restoration

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stochastic Distributed Protocol for Electric Vehicle Charging with Discrete Charging Rate

Stochastic Distributed Protocol for Electric Vehicle Chargin...

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General Meeting of the IEEE-Power-and-Energy-Society

作者： Gan, Lingwen Topcu, Ufuk Low, Steven H. CALTECH Pasadena CA 91125 USA

ISBN: (纸本)9781467327299

To address the grid-side challenges associated with the anticipated high electric vehicle (EV) penetration level, various charging protocols have been proposed in the literature. Most if not all of these protocols assume continuous charging rates and allow intermittent charging. However, due to charging technology limitations, EVs can only be charged at a fixed rate, and the intermittency in charging shortens the battery lifespan. We consider these charging requirements, and formulate EV charging scheduling as a discrete optimization problem. We propose a stochastic distributed algorithm to approximately solve the optimal EV charging scheduling problem in an iterative procedure. In each iteration, the transformer receives charging profiles computed by the EVs in the previous iteration, and broadcasts the corresponding normalized total demand to the EVs;each EV generates a probability distribution over its potential charging profiles accordingly, and samples from the distribution to obtain a new charging profile. We prove that this stochastic algorithm almost surely converges to one of its equilibrium charging profiles, and each of its equilibrium charging profiles has a negligible sub-optimality ratio. Case studies corroborate our theoretical results.

关键词： distributed control discrete optimization stochastic algorithm electric vehicle charging

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LINEAR CONVERGENCE OF stochastic BLOCK-COORDINATE FIXED POINT algorithmS 26

LINEAR CONVERGENCE OF STOCHASTIC BLOCK-COORDINATE FIXED POIN...

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26th European Signal Processing Conference (EUSIPCO)

作者： Combettes, Patrick L. Pesquet, Jean-Christophe North Carolina State Univ Dept Math Box 8205 Raleigh NC 27695 USA Univ Paris Saclay Cent Supelec INRIA Ctr Visual Comp Gif Sur Yvette France

ISBN: (纸本)9789082797015

Recent random block-coordinate fixed point algorithms are particularly well suited to large-scale optimization in signal and image processing. These algorithms feature random sweeping rules to select arbitrarily the blocks of variables that are activated over the course of the iterations and they allow for stochastic errors in the evaluation of the operators. The present paper provides new linear convergence results. These convergence rates are compared to those of standard deterministic algorithms both theoretically and experimentally in an image recovery problem.

关键词： Block-coordinate algorithm fixed-point algorithm linear convergence stochastic algorithm

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stochastic Speculative Computation Method on general purpose graphics processing units 6

Stochastic Speculative Computation Method on general purpose...

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6th IIAI International Congress on Advanced Applied Informatics (IIAI-AAI)

作者： Suzuki, Yosuke Hamada, Akira Iizuka, Yasuki Tokai Univ Grad Sch Sci 4-1-1 Kitakaname Hiratsuka Kanagawa 2591292 Japan

ISBN: (纸本)9781538606216

Parallel processing is considered effective in order to solve problems with significant computational complexity. The development of graphics processing units (GPU) in recent years has led to eneral purpose GPU (GPGPU) and brought significant benefits to the AI research field. In conventional parallel processing, processes must be frequently synchronized;thus, parallel computing does not necessarily improve the efficiency of computation except for special algorithms designed for parallel computation. In this study, we investigate the effect of applying MultiStart based speculative computation on GPGPU. This method incurs little synchronization overhead. Although the effect of this method is stochastic, an expected value is theoretically calculable. We analyze theoretically about the effects of the speculative method, and provide the results of applying the method to combinatorial optimization problems.

关键词： speculative computing parallel processing stochastic algorithm

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A Constant-Factor Approximation for stochastic Steiner Forest

A Constant-Factor Approximation for Stochastic Steiner Fores...

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41st Annual ACM Symposium on Theory of Computing

作者： Gupta, Anupam Kumar, Amit Carnegie Mellon Univ Dept Comp Sci Pittsburgh PA 15213 USA

ISBN: (纸本)9781605586137

We consider the stochastic Steinerforest problem: suppose we were given it collection of Steiner forest instances, and were guaranteed that a random one of these instances would appear tomorrow;moreover the cost of edges tomorrow will he lambda times Hie, cost. of edges today. Which edges should we buy today so that we call extend it to a solution for the instance arriving tomorrow, to minimize, the expected total cost? While very general results have been developed for man, v problems in stochastic discrete optimization over the past, years, the approximation status of the stochastic Steiner Forest problem has remained open, with previous works Yielding constant-factor approximations only for special cases. We resolve the status of this problem by giving a constant-factor primal-dual based approximation algorithm.

关键词： Approximation algorithms stochastic algorithm

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