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A Variance Reducing Stochastic proximal Method with Acceleration Techniques

Tsinghua Science and Technology 2023年第6期28卷 999-1008页

作者： Jialin Lei Ying Zhang Zhao Zhang School of Mathematical Science Zhejiang Normal UniversityJinhua 321004China

We consider a fundamental problem in the field of machine learning—structural risk minimization,which can be represented as the average of a large number of smooth component functions plus a simple and convex(but possibly non-smooth)*** this paper,we propose a novel proximal variance reducing stochastic method building on the introduced *** method achieves two proximal operator calculations by combining the fast Douglas–Rachford splitting and refers to the scheme of the FISTA algorithm in the choice of momentum *** show that the objective function value converges to the iteration point at the rate of O(1/k)when each loss function is convex and *** addition,we prove that our method achieves a linear convergence rate for strongly convex and smooth loss *** demonstrate the effectiveness of the proposed algorithm,especially when the loss function is ill-conditioned with good acceleration.

关键词： composite optimization Variance Reduction(VR) fast Douglas–Rachford(DR)splitting proximal operator

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An Efficient Smoothing and Thresholding Image Segmentation Framework with Weighted Anisotropic-Isotropic Total Variation

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Communications on Applied Mathematics and Computation 2024年第2期6卷 1369-1405页

作者： Kevin Bui Yifei Lou Fredrick Park Jack Xin Department of Mathematics University of CaliforniaIrvineIrvineCA 92697-3875USA Department of Mathematics University of North CarolinaChapel HillChapel HillNC 27599.USA Department of Mathematics and Computer Science Whittier CollegeWhittierCA 90602USA

In this paper,we design an efficient,multi-stage image segmentation framework that incorporates a weighted difference of anisotropic and isotropic total variation(AITV).The segmentation framework generally consists of two stages:smoothing and thresholding,thus referred to as smoothing-and-thresholding(SaT).In the first stage,a smoothed image is obtained by an AITV-regularized Mumford-Shah(MS)model,which can be solved efficiently by the alternating direction method of multipliers(ADMMs)with a closed-form solution of a proximal operator of the l_(1)-αl_(2) *** convergence of the ADMM algorithm is *** the second stage,we threshold the smoothed image by K-means clustering to obtain the final segmentation *** experiments demonstrate that the proposed segmentation framework is versatile for both grayscale and color images,effcient in producing high-quality segmentation results within a few seconds,and robust to input images that are corrupted with noise,blur,or *** compare the AITV method with its original convex TV and nonconvex TVP(O

关键词： Image segmentation Non-convex optimization Mumford-Shah(MS)model Alternating direction method of multipliers(ADMMs) proximal operator

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PAPR Reduction in Massive MU-MIMO-OFDM Systems Using the proximal Gradient Method

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Journal of Communications and Information Networks 2019年第1期4卷 88-94页

作者： Davinder Singh R.K.Sarin Department of Electronics and Communication Engineering Dr.B.R.Ambedkar National Institute of TechnologyJalandharPunjabIndia-144011

In this paper,we address the issue of peak-to-average power ratio(PAPR)reduction in large-scale multiuser multiple-input multiple-output(MU-MIMO)orthogonal frequency-division multiplexing(OFDM)*** reduction and the multiuser interference(MUI)cancellation problem are jointly formulated as an l_(∞)-norm based composite convex optimization problem,which can be solved efficiently using the iterative proximal gradient *** proximal operator associated with l_(∞)-norm is evaluated using a low-cost sorting *** proposed method adaptively chooses the step size to accelerate *** results reveal that the proximal gradient method converges swiftly while provid-ing considerable PAPR reduction and lower out-of-band radiation.

关键词： OFDM MU-MIMO PAPR reduction proximal operator proximal gradient method

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Analysis of loss functions in support vector machines

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Frontiers of Mathematics in China 2023年第6期18卷 381-414页

作者： Huajun WANG Naihua XIU Department of Mathematics School of ScienceBeijing Jiaotong UniversityBeijing 100044China

Support vector machines(SVMs)are a kind of important machine learning methods generated by the cross interaction of statistical theory and optimization,and have been extensively applied into text categorization,disease diagnosis,face detection and so *** loss function is the core research content of SVM,and its variational properties play an important role in the analysis of optimality conditions,the design of optimization algorithms,the representation of support vectors and the research of dual *** paper summarizes and analyzes the 0-1 loss function and its eighteen popular surrogate loss functions in SVM,and gives three variational properties of these loss functions:subdifferential,proximal operator and Fenchel conjugate,where the nine proximal operators and fifteen Fenchel conjugates are given by this paper.

关键词： Support vector machines loss function subdifferential proximal operator Fenchel conjugate

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