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Finite-sum smooth optimization with SARAH

COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2022年第3期82卷 561-593页

作者： Nguyen, Lam M. van Dijk, Marten Phan, Dzung T. Nguyen, Phuong Ha Weng, Tsui-Wei Kalagnanam, Jayant R. IBM Res Thomas J Watson Res Ctr Yorktown Hts NY 10598 USA CWI Comp Secur Grp Amsterdam Netherlands eBay Inc San Jose CA USA Univ Calif San Diego La Jolla CA 92093 USA

We introduce NC-SARAH for non-convex optimization as a practical modified version of the original SARAH algorithm that was developed for convex optimization. NC-SARAH is the first to achieve two crucial performance properties at the same time-allowing flexible minibatch sizes and large step sizes to achieve fast convergence in practice as verified by experiments. NC-SARAH has a close to optimal asymptotic convergence rate equal to existing prior variants of SARAH called SPIDER and SpiderBoost that either use an order of magnitude smaller step size or a fixed minibatch size. For convex optimization, we propose SARAH++ with sublinear convergence for general convex and linear convergence for strongly convex problems;and we provide a practical version for which numerical experiments on various datasets show an improved performance.

关键词： Finite-sum Smooth Non-convex Convex stochastic algorithm Variance reduction

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Search for minimum aberration designs with uniformity

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ANNALS OF THE INSTITUTE OF STATISTICAL MATHEMATICS 2022年第2期74卷 271-287页

作者： Jiang, Bochuan Wang, Yaping Ai, Mingyao Beijing Jiaotong Univ Sch Sci Beijing 100044 Peoples R China East China Normal Univ KLATASDS MOE Shanghai 200062 Peoples R China Peking Univ Sch Math Sci LMAM Beijing 100871 Peoples R China Peking Univ Ctr Stat Sci Beijing 100871 Peoples R China

Uniform designs have been widely applied in engineering and sciences' innovation. When a lot of quantitative factors are investigated with as few runs as possible, a supersaturated uniform design with good overall and projection uniformity is needed. By combining combinatorial methods and stochastic algorithms, such uniform designs with flexible numbers of columns are constructed in this article under the wrap-around L-2-discrepancy. Compared with the existing designs, the new designs and their two-dimensional projections not only have less aberration, but also have lower discrepancy. Furthermore, some novel theoretical results on the minimum-aberration, uniform and uniform projection designs are obtained.

关键词： Discrepancy Projection stochastic algorithm Uniform design

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Experiments with repeating weighted boosting search for optimization in signal processing applications

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IEEE TRANSACTIONS ON SYSTEMS MAN AND CYBERNETICS PART B-CYBERNETICS 2005年第4期35卷 682-693页

作者： Chen, S Wang, XX Harris, CJ Univ Southampton Sch Elect & Comp Sci Southampton SO17 1BJ Hants England Aston Univ Neural Comp Res Grp Birmingham B4 7ET W Midlands England

Many signal processing applications pose optimization problems with multimodal and nonsmooth cost functions. Gradient methods are ineffective in these situations, and optimization methods that require no gradient and can achieve a global optimal solution are highly desired to tackle these difficult problems. The paper proposes a guided global search optimization technique, referred to as the repeated weighted boosting search. The proposed optimization algorithm is extremely simple and easy to implement, involving a minimum programming effort. Heuristic explanation is given for the global search capability of this technique. Comparison is made with the two better known and widely used guided global search techniques, known as the genetic algorithm and adaptive simulated annealing, in terms of the requirements for algorithmic parameter tuning. The effectiveness of the proposed algorithm as a global optimizer are investigated through several application examples.

关键词： adaptive simulated annealing boosting evolutionary computation genetic algorithm global search multistart optimization stochastic algorithm

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Exact simulation of the first passage time through a given level of jump diffusions?

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MATHEMATICS AND COMPUTERS IN SIMULATION 2023年 203卷 553-576页

作者： Herrmann, Samuel Massin, Nicolas Univ Bourgogne Franche Comte Inst Math Bourgogne IMB UMR 5584 CNRS F-21000 Dijon France

Continuous-time stochastic processes play an important role in the description of random phenomena. It is therefore important to study particular stopping times dependent on the trajectories of these processes. Two approaches are possible: introducing an explicit expression of their probability distribution, and evaluating values generated by numerical models. Choosing the second alternative, we propose an algorithm to generate the first passage time through a given level. The stochastic process under consideration is a one-dimensional jump diffusion that satisfies a stochastic differential equation driven by a Brownian motion. It is subject to random shocks that are characterised by an independent Poisson process. The proposed algorithm belongs to the family of rejection sampling procedures: the outcome of the algorithm and the stopping time under consideration are identically distributed. This algorithm is based on both the exact simulation of the diffusion value at a fixed time and on the exact simulation of the first passage time for continuous diffusion processes (see Herrmann and Zucca (2019)). At a fixed point in time, the main challenge is to generate the position of a continuous diffusion that is conditioned not to reach a given level before that time. We present the construction of the algorithm and numerical examples. We also discuss specific conditions leading to the recurrence of a jump diffusion process. (c) 2022 International Association for Mathematics and Computers in Simulation (IMACS). Published by Elsevier B.V. All rights reserved.

关键词： First passage time Jump diffusion Girsanov formula Rejection sampling Bessel process stochastic algorithm

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Producing dense packings of cubes

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DISCRETE MATHEMATICS 2008年第22期308卷 5230-5245页

作者： Gensane, Thierry Ryckelynck, Philippe Lab Math Pures & Appl Joseph Liouville F-62228 Calais France

In this paper we consider the problem of packing a set of d-dimensional congruent cubes into a sphere of smallest radius. We describe and investigate an approach based on a function psi called the maximal inflation function. In the three-dimensional case, we localize the contact between two inflated cubes and we thus improve the efficiency of calculating psi. This approach and a stochastic algorithm are used to find dense packings of cubes in 3 dimensions up to n = 20. For example, we obtain a packing of eight cubes that improves on the cubic lattice packing. (C) 2007 Elsevier B.V. All rights reserved.

关键词： cubes packings inflation of cubes stochastic algorithm

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Toward integrated design of additive manufacturing through a process development model and multi-objective optimization

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INTERNATIONAL JOURNAL OF ADVANCED MANUFACTURING TECHNOLOGY 2018年第9-12期96卷 4145-4164页

作者： Asadollahi-Yazdi, Elnaz Gardan, Julien Lafon, Pascal Univ Technol Troyes UMR CNRS 6281 ICD LASMIS 12 Rue Marie Curie BP2060 F-10010 Troyes France EPF Engn Sch 2 Rue Fernand SASTRE F-10430 Rosiere Pres Troyes France

This paper deals with design for manufacturing (DFM) approach for additive manufacturing (AM) to investigate simultaneously the different attributes and criteria of design and manufacturing. The integrated design approach is provided in the product definition level and it gradually maps the customer requirements to the final product model. The main contribution of this paper is an interface processing engine that is an interface between the product model and manufacturing model. This study uses the Skin-Skeleton approach to model the first definition of the product and model the material flow of AM technology as the manufacturing process. This engine is developed through analysis of all AM technologies and identification of their parameters, criteria, and drawbacks. In order to evaluate some product and process parameters, a multi-objective problem is formulated based on the analysis of all AM technologies;production time and material mass are optimized regarding mechanical behavior of the material and roughness of product. The approach is validated by a case study through a bag hook example. From its requirement specification to the proposed approach, this article defines an optimized product and its manufacturing parameters for fused deposition modeling (FDM) technology.

关键词： Additive manufacturing Design for manufacturing Skin-Skeleton approach Multi-objective optimization problem stochastic algorithm Fused deposition modeling

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Thin-film designs by simulated annealing

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APPLIED OPTICS 1996年第31期35卷 6219-6226页

作者： Boudet, T Chaton, P Herault, L Gonon, G Jouanet, L Keller, P Grenoble Nuclear Research Center 17 rue des Martyrs 38054 Grenoble Cedex 9 France Laboratoire d'Electronique de Technologie et d'Instrumentation Commissariat a l'Energie Atomique Département Optrònique Couches Minces pour l'Optique Grenoble Nuclear Research Center 17 rue des Martyrs 38054 Grenoble Cedex 9 France Laboratoire d'Electronique de Technologie et d'Instrumentation Commissariat a l'Energie Atomique Département Système Grenoble Nuclear Research Center 17 rue des Martyrs 38054 Grenoble Cedex 9 France

With the increasing power of computers, new methods in synthesis of optical multilayer systems have appeared. Among these, the simulated-annealing algorithm has proved its efficiency in several fields of physics. We propose to show its performances in the field of optical multilayer systems through different (C) 1996 Optical Society of America

关键词： optical thin films synthesis stochastic algorithm simulated annealing

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An improved Tabu search for the global optimizations of electromagnetic devices

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IEEE TRANSACTIONS ON MAGNETICS 2001年第5期37卷 3570-3574页

作者： Ho, SL Yang, SY Ni, GZ Wong, HC Hong Kong Polytech Univ EE Dept Hong Kong Hong Kong Peoples R China Hong Kong Polytech Univ Ind Ctr Hong Kong Hong Kong Peoples R China

An extended Tabu algorithm with an aspiration factor is proposed. The algorithm is based on the success of techniques such as the memorization of the previously visited subspaces, the systematic diversification as well as the intensification process for neighborhood creations. The numerical results obtained by solving a mathematical test function and the benchmark problem 22 of the TEAM Workshop reported in this paper will demonstrate the usefulness of the proposed method.

关键词： global optimization inverse problem optimal design stochastic algorithm tabu search method

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An Improved Cross-Entropy Method Applied to Inverse Problems

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IEEE TRANSACTIONS ON MAGNETICS 2012年第2期48卷 327-330页

作者： An, Siguang Yang, Shiyou Ho, S. L. Ni, Peihong Zhejiang Univ Coll Elect Engn Hangzhou 310027 Peoples R China China Jiliang Univ Dept Elect Engn Hangzhou 310018 Peoples R China Hong Kong Polytech Univ Dept Elect Engn Hong Kong Hong Kong Peoples R China

An improved cross-entropy method for global optimizations of inverse problems with continuous variables is proposed. To enhance the convergence speed, improvements on both algorithm development and iterative process are introduced. To monitor and guide the searching process, the design space is divided into subdomains and three indicators are assigned for each subdomain in order to evaluate its performances. To balance exploitation and exploration searches, the whole iterative process is divided a diversification and an intensification phase. In the diversification phase, a novel mechanism is introduced to increase the sampling diversity to avoid the solution being trapped onto a local optimum;in the intensification phase, the strategy of shifting away from the worst subdomains equips the algorithm with enhanced convergence rates. The proposed method is applied to a mathematical function and the TEAM Workshop problem 22. Comparisons with its counterparts are made to demonstrate the effectiveness of the proposed work.

关键词： Cross-entropy method global optimization stochastic algorithm TEAM workshop problem

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A Modified Tabu Search Method Applied to Inverse Problems

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IEEE TRANSACTIONS ON MAGNETICS 2011年第5期47卷 1234-1237页

作者： An, Siguang Yang, Shiyou Ho, S. L. Li, Tao Fu, Weinong Zhejiang Univ Coll Elect Engn Hangzhou 310027 Zhejiang Peoples R China Hong Kong Polytech Univ Dept Elect Engn Hong Kong Hong Kong Peoples R China

A modified tabu search method for global optimizations of inverse problems is presented. In the proposed algorithm, the whole search procedure is divided into three different phases: intensification, diversification, and refinement. Two "new point generating mechanisms" as well as a "dynamic parameters updating" rule are proposed to improve the searching efficiency without compromising the solution's accuracy. Numerical results on TEAM Workshop Problems 22 and 25 are used to demonstrate the effectiveness and advantages of the proposed method.

关键词： Global optimization stochastic algorithm tabu search (TS) TEAM Workshop Problem

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