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arXiv 2024年

作者： Li, Qiang Wai, Hoi-To Dept. of System Engineering & Engineering Management Faculty of Engineering The Chinese University of Hong Kong Shatin District Hong Kong

This paper studies the effect of data homogeneity on multi-agent stochastic optimization. We consider the decentralized stochastic gradient (DSGD) algorithm and perform a refined convergence analysis. Our analysis is explicit on the similarity between Hessian matrices of local objective functions which captures the degree of data homogeneity. We illustrate the impact of our analysis through studying the transient time, defined as the minimum number of iterations required for a distributed algorithm to achieve comparable performance as its centralized counterpart. When the local objective functions have similar Hessian, the transient time of DSGD can be as small as O(n2/3/ρ8/3) for smooth (possibly non-convex) objective functions, O(√n/ρ) for strongly convex objective functions, where n is the number of agents and ρ is the spectral gap of graph. These findings provide a theoretical justification for the empirical success of DSGD. Our analysis relies on a novel observation with higher-order Taylor approximation for gradient maps that can be of independent interest. Numerical simulations validate our findings. © 2024, CC BY.

关键词： optimization algorithms

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Second-Order Adjoint-Based Control for Multiphase Flow in Subsurface Oil Reservoirs

Second-Order Adjoint-Based Control for Multiphase Flow in Su...

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2010 49th IEEE Conference on Decision and Control

作者： Eka Suwartadi Stein Krogstad Bjarne Foss Department of Engineering Cybernetics Norwegian University of Science and Technology 7491 Trondheim Norway Department of Applied Mathematics SINTEF ICT Blindern 0314 Oslo Norway

ISBN: (纸本)9781424477456

This paper presents an efficient way to compute second-order gradients by using the adjoint method for PDE-constrained optimization. The gradient thus obtained will then be used in an optimization algorithm. We propose a conjugate gradient combined with the trust-region method, which may have a quadratic convergence rate of Newton's method. Furthermore, we compare the proposed algorithm to a quasi-Newton method (BFGS). We apply the method for production optimization of oil reservoirs. Two numerical cases are presented, showing that our proposed method requires fewer function and gradient evaluations.

关键词： multiphase flow OIL RESERVOIR OIL FIELD Newton method Production optimization optimization algorithms Quadratic Convergence conjugate gradient

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Parameter Study on Improved Quantum-behaved Particle Swarm optimizations

Parameter Study on Improved Quantum-behaved Particle Swarm O...

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2017 2nd International Conference on Applied Mathematics, Simulation and Modelling(AMSM2017)

作者： Yi FU Zhi-guo CHEN Ji ZHAO Juan MEI School of Internet of Things Engineering Wuxi City College of Vocational Technology WuXi Research Center for Environmental Science & Engineering School of Internet of Things Engineering Jiangnan University

Inspired by concepts in quantum mechanics and particle swarm optimization(PSO) algorithm,quantum-behaved particle swarm optimization(QPSO) algorithm was proposed as a variant of PSO algorithm with better global search *** the same time,some improved QPSO algorithms are also *** order to determine whether the performance of the algorithm is affected by the location of the parameter,this paper compares four variants of QPSO *** operator is exerted on the mean best position and the particle's previous position to improve the search ability of the QPSO algorithm,***,some empirical studies on popular benchmark functions are performed in order to make a full performance evaluation and comparison among four variants of QPSO *** experimental results show that the new parameter based on individual particles evolutionary process which located in the mean best position algorithm(IEQPSO-1) is more effective approach than others in most cases.

关键词： Quantum-behaved particle swarm optimization Swarm intelligence optimization algorithms

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CMA-ES with Optimal Covariance Update and Storage Complexity 16

CMA-ES with Optimal Covariance Update and Storage Complexity

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Annual Conference on Neural Information Processing Systems

作者： Oswin Krause Didac R. Arbones Christian Igel Dept. of Computer Science University of Copenhagen Copenhagen Denmark

ISBN: (纸本)9781510838819

The covariance matrix adaptation evolution strategy (CMA-ES) is arguably one of the most powerful real-valued derivative-free optimization algorithms, finding many applications in machine learning. The CMA-ES is a Monte Carlo method, sampling from a sequence of multi-variate Gaussian distributions. Given the function values at the sampled points, updating and storing the covariance matrix dominates the time and space complexity in each iteration of the algorithm. We propose a numerically stable quadratic-time covariance matrix update scheme with minimal memory requirements based on maintaining triangular Cholesky factors. This requires a modification of the cumulative step-size adaption (CSA) mechanism in the CMA-ES, in which we replace the inverse of the square root of the covariance matrix by the inverse of the triangular Cholesky factor. Because the triangular Cholesky factor changes smoothly with the matrix square root, this modification does not change the behavior of the CMA-ES in terms of required objective function evaluations as verified empirically. Thus, the described algorithm can and should replace the standard CMA-ES if updating and storing the covariance matrix matters.

关键词： variance covariance matrix Covariance matrix Square root Cholesky Inverse Gaussian distribution space complexities Triangular memory requirements optimization algorithms

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Fast algorithms for Fourier extension based on boundary interval data

arXiv

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arXiv 2024年

作者： Zhao, Zhenyu Wang, Yanfei School of Mathematics and Statistics Shandong University of Technology Zibo255049 China Key Laboratory of Petroleum Resources Research Institute of Geology and Geophysics Chinese Academy of Sciences Beijing100029 China

This paper present a new algorithm for the computation of Fourier extension based on boundary data, which can obtain a super-algebraic convergent Fourier approximation for non-periodic functions. The algorithm calculates the extension part through boundary data and connects it with the original function to form a periodic smooth function. By testing the key parameters involved, their impact on the algorithm is clarified and the optimization setting scheme of the parameters is proposed. Compared with FFT, the algorithm only needs to increase the computational complexity by a fixed small amount. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

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TERIME: An improved RIME algorithm with enhanced exploration and exploitation for robust parameter extraction of photovoltaic models

arXiv

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arXiv 2024年

作者： Chen, Shi-Shun Jiang, Yu-Tong Chen, Wen-Bin Li, Xiao-Yang School of Reliability and Systems Engineering Beihang University Beijing100191 China

Parameter extraction of photovoltaic (PV) models is crucial for the planning, optimization, and control of PV systems. Although some methods using meta-heuristic algorithms have been proposed to determine these parameters, the robustness of solutions obtained by these methods faces great challenges when the complexity of the PV model increases. The unstable results will affect the reliable operation and maintenance strategies of PV systems. In response to this challenge, an improved RIME algorithm with enhanced exploration and exploitation is proposed for robust and accurate parameter identification for various PV models. Specifically, the differential evolution mutation operator is integrated in the exploration phase to enhance the population diversity. Meanwhile, a new exploitation strategy incorporating randomization and neighborhood strategies simultaneously is developed to maintain the balance of exploitation width and depth. The improved RIME algorithm is applied to estimate the optimal parameters of the single-diode model (SDM), double-diode model (DDM), and triple-diode model (TDM) combined with the Lambert-W function for three PV cell and module types including RTC France, Photo Watt-PWP 201 and S75. According to the statistical analysis in 100 runs, the TEIMRE achieves more accurate and robust parameter estimations than other techniques to various PV models in varying environmental conditions. All of our source codes are publicly available at https://***/dirge1/TERIME. © 2024, CC BY.

关键词： optimization algorithms

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Independent Component Analysis of EEG-fMRI data for studying epilepsy and epileptic seizures

Independent Component Analysis of EEG-fMRI data for studying...

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Annual International Conference of the IEEE Engineering in Medicine and Biology Society

作者： Tiziana Franchin Maria G. Tana Vittorio Cannata Sergio Cerutti Anna M. Bianchi Clinical-Technological Innovations Research Unit Bambino Gesu Children's Hospital and Research

ISBN: (纸本)9781457702150

Here we present a method for classifying fMRI independent components (ICs) by using an optimized algorithm for the individuation of noisy signals from sources of interest. The method was applied to estimate brain activations from combined EEG-fMRI data for the exploration of epilepsy. Spatial ICA was performed using the above-mentioned optimized algorithm and other three popular algorithms. ICs were sorted considering the value: of the coefficients of determination R2, obtained from the multiple regression analysis with morphometric maps of cerebral matter;of the kurtosis, which features the signal energy. The validation of the method was performed comparing the brain activations obtained with those resulted using the General Linear Model (GLM). The ICA-derived activations in different datasets comprised subareas of the GLM-revealed activations, even if the volume and the shape of activated areas do not correspond exactly. The method proposed also detects additional negative regions implicated in a default mode of brain activity, and not clearly identified by GLM. Compared with a traditional GLM approach, the ICA one provides a flexible way to analyze fMRI data that reduces the assumptions placed upon the hemodynamic response of the brain and the temporal constrains.

关键词： optimization algorithms epileptic seizure Cerebrum signal energy Individuation Epilepsy Integrated circuits kurtosis brain activity fMRI

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Heterogeneous Visual Features Fusion via Sparse Multimodal Machine

Heterogeneous Visual Features Fusion via Sparse Multimodal M...

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IEEE Conference on Computer Vision and Pattern Recognition

作者： Hua Wang Feiping Nie Heng Huang Chris Ding Department of Electrical Engineering and Computer Science Colorado School of Mines Department of Computer Science and Engineering University of Texas at Arlington

ISBN: (纸本)9781467364102

To better understand, search, and classify image and video information, many visual feature descriptors have been proposed to describe elementary visual characteristics, such as the shape, the color, the texture, etc. How to integrate these heterogeneous visual features and identify the important ones from them for specific vision tasks has become an increasingly critical problem. In this paper, We propose a novel Sparse Multimodal Learning (SMML) approach to integrate such heterogeneous features by using the joint structured sparsity regularizations to learn the feature importance of for the vision tasks from both group-wise and individual point of views. A new optimization algorithm is also introduced to solve the non-smooth objective with rigorously proved global convergence. We applied our SMML method to five broadly used object categorization and scene understanding image data sets for both single-label and multi-label image classification tasks. For each data set we integrate six different types of popularly used image features. Compared to existing scene and object categorization methods using either single modality or multi-modalities of features, our approach always achieves better performances measured.

关键词： Visualization video information Integrate image feature Religious Missions global convergence optimization algorithms Sight

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Interconnection Conditions for the Stability of Nonlinear Sampled-Data Extremum Seeking Schemes

Interconnection Conditions for the Stability of Nonlinear Sa...

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IEEE Conference on Decision and Control

作者： Karla Kvaternik Lacra Pavel Edward S. Rogers Department of Electrical and Computer Engineering University of Toronto

ISBN: (纸本)9781612848006

The application of numerical optimization methods to the problem of extremum seeking control (ESC) has the potential to greatly diversify the types and capabilities of ESC schemes. The first uniform treatment of such sampled-data ESC schemes was given in [1]. We approach the problem from the point of view of interconnected systems' theory, deriving a different, more structurally concrete set of conditions that guarantee the closed-loop stability of such schemes. Our main assumptions concern the interconnection terms arising from the dynamic coupling between a numerical optimization algorithm and a continuous-time nonlinear plant. We demonstrate how these assumptions are satisfied for a special case involving an approximate gradient descent. Our primary motivation in deriving these new conditions is their natural suitability for the development and analysis of decentralized ESC schemes.

关键词： optimization algorithms Data sampling extremum values Scheme optimization methods

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Model Predictive Control for Constrained Discrete Time Systems: An Integrated Perturbation Analysis and Sequential Quadratic Programming Approach

Model Predictive Control for Constrained Discrete Time Syste...

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Proceedings of the 46th IEEE Conference on Decision and Control, Pages 2759-3219

作者： Reza Ghaemi Jing Sun Ilya Kolmanovsky Department of Electrical Engineering and Computer Science and the Department of Naval Architecture and Marine Engineering University of Michigan Ann Arbor MI USA University of Michigan USA

ISBN: (纸本)9781424414970;1424414970

Further improvements in computational efficiency of numerical optimization algorithms is a promising venue to extend the applicability of Model Predictive Control (MPC) to broader classes of embedded systems with fast dynamics and limited computing resources. Along these lines, we develop a novel numerical optimization algorithm based on Integrated Perturbation Analysis and Sequential Quadratic Programming (IPA-SQP), which exploits special structure of the optimization problem and complementary features of Perturbation Analysis and SQP methods, to improve computational efficiency in general MPC problems with mixed state and input constraints. An example is reported to illustrate the reduction in on-line computing time achieved with IPA-SQP approach.

关键词： optimization algorithms sequential quadratic programming Computational efficiency Model predictive control Predictive control perturbation discrete time systems Structural optimization Special structures vortex state (superconductivity) Maximum Allowable Concentration Embedded systems quadratic programming

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