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On the convergence of splitting algorithm for mixed equilibrium problems on Hadamard manifolds

JOURNAL OF MATHEMATICAL CHEMISTRY 2020年第4期58卷 799-815页

作者： Khammahawong, K. Kumam, P. Chaipunya, P. KMUTT Dept Math 126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT KMUTTFixed Point Res Lab KMUTTFixed Point Theory & Applicat Res Grp Dept MathFac Sci 126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT Ctr Excellence Theoret & Computat Sci TaCS CoE SCL 802 Fixed Point Lab Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand

The aim of this paper is to introduce a splitting algorithm to solving mixed equilibrium problems on a Hadamard manifold. The convergence of the sequence generated by the proposed algorithm is established under suitab... 详细信息

关键词： Equilibrium problems Hadamard manifolds Monotonicity proximal algorithm Splitting algorithm

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A Variational Method for Dejittering Large Fluorescence Line Scanner Images

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IEEE TRANSACTIONS ON COMPUTATIONAL IMAGING 2018年第2期4卷 241-256页

作者： Hoai-Nam Nguyen Paveau, Vincent Cauchois, Cyril Kervrann, Charles INRIA Ctr Rennes Bretagne Atlantique F-35042 Rennes France Innopsys Inc F-31390 Carbonne France

We propose a variational method dedicated to jitter correction of large fluorescence scanner images. Our method consists in minimizing a global energy functional to estimate a dense displacement field representing the spatially-varying jitter. The computational approach is based on a half-quadratic splitting of the energy functional, which decouples the realignment data term and the dedicated differential-based regularizer. The resulting problem amounts to alternatively solving two convex and nonconvex optimization subproblems with appropriate algorithms. Experimental results on artificial and large real fluorescence images demonstrate that our method is not only capable to handle large displacements but is also efficient in terms of subpixel precision without inducing additional intensity artifacts.

关键词： Dejittering fluorescence scanner variational method regularization optimization quadratic relaxation proximal algorithm

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Rectifiability of Self-Contracted Curves in the Euclidean Space and Applications

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JOURNAL OF GEOMETRIC ANALYSIS 2015年第2期25卷 1211-1239页

作者： Daniilidis, A. David, G. Durand-Cartagena, E. Lemenant, A. Univ Chile Dept Ingn Matemat Santiago Chile Univ Paris 11 Math Lab UMR 8628 F-91405 Orsay France Inst Univ France Paris France UNED ETSI Ind Dept Matemat Aplicada Madrid 28040 Spain Univ Paris 07 UFR Math F-75205 Paris 13 France

It is hereby established that, in Euclidean spaces of finite dimension, bounded self-contracted curves have finite length. This extends the main result of Daniilidis et al. (J. Math. Pures Appl. 94: 183-199, 2010) concerning continuous planar self-contracted curves to any dimension, and dispenses entirely with the continuity requirement. The proof borrows heavily from a geometric idea of Manselli and Pucci (Geom. Dedic. 38:211-227, 1991) employed for the study of regular enough curves, and can be seen as a nonsmooth adaptation of the latter, albeit a nontrivial one. Applications to continuous and discrete dynamical systems are discussed: continuous self-contracted curves appear as generalized solutions of nonsmooth convex foliation systems, recovering a hidden regularity after reparameterization, as a consequence of our main result. In the discrete case, proximal sequences (obtained through implicit discretization of a gradient system) give rise to polygonal self-contracted curves. This yields a straightforward proof for the convergence of the exact proximal algorithm, under any choice of parameters.

关键词： Self-contracted curve Rectifiable curve Convex foliation Secant Self-expanded curve proximal algorithm

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Relaxed inertial methods for solving the split monotone variational inclusion problem beyond co-coerciveness

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OPTIMIZATION 2023年第2期72卷 607-646页

作者： Izuchukwu, Chinedu Reich, Simeon Shehu, Yekini Technion Israel Inst Technol Dept Math Haifa Israel Zhejiang Normal Univ Dept Math Jinhua Zhejiang Peoples R China

We study the split monotone variational inclusion problem in two real Hilbert spaces. Combining the inertial and relaxation techniques with the proximal contraction algorithm, we propose two new methods for solving th... 详细信息

关键词： Contraction method Lipschitz continuous monotone opearator proximal algorithm relaxed inertial method split monotone variational inclusion problem

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Integrating spatial-anatomical regularization and structure sparsity into SVM: Improving interpretation of Alzheimer's disease classification

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NEUROIMAGE 2018年 178卷 445-460页

作者： Sun, Zhuo Qiao, Yuchuan Lelieveldt, Boudewijn P. F. Staring, Marius Leiden Univ Dept Radiol Div Image Proc Med Ctr NL-2300 RC Leiden Netherlands Delft Univ Technol Fac EEMCS Intelligent Syst Grp NL-2600 GA Delft Netherlands

In recent years, machine learning approaches have been successfully applied to the field of neuroimaging for classification and regression tasks. However, many approaches do not give an intuitive relation between the raw features and the diagnosis. Therefore, they are difficult for clinicians to interpret. Moreover, most approaches treat the features extracted from the brain (for example, voxelwise gray matter concentration maps from brain MRI) as independent variables and ignore their spatial and anatomical relations. In this paper, we present a new Support Vector Machine (SVM)-based learning method for the classification of Alzheimer's disease (AD), which integrates spatial-anatomical information. In this way, spatial-neighbor features in the same anatomical region are encouraged to have similar weights in the SVM model. Secondly, we introduce a group lasso penalty to induce structure sparsity, which may help clinicians to assess the key regions involved in the disease. For solving this learning problem, we use an accelerated proximal gradient descent approach. We tested our method on the subset of ADNI data selected by Cuingnet et al. (2011) for Alzheimer's disease classification, as well as on an independent larger dataset from ADNI. Good classification performance is obtained for distinguishing cognitive normals (CN) vs. AD, as well as on distinguishing between various sub-types (e.g. CN vs. Mild Cognitive Impairment). The model trained on Cuignet's dataset for AD vs. CN classification was directly used without re-training to the independent larger dataset. Good performance was achieved, demonstrating the generalizability of the proposed methods. For all experiments, the classification results are comparable or better than the state-of-the-art, while the weight map more clearly indicates the key regions related to Alzheimer's disease.

关键词： Alzheimer's disease Support vector machine (SVM) Spatial-anatomical regularization Structure sparsity proximal algorithm

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Convex Variational Formulation with Smooth Coupling for Multicomponent Signal Decomposition and Recovery

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Numerical Mathematics(Theory,Methods and Applications) 2009年第4期2卷 485-508页

作者： Luis M.Briceo-Arias Patrick L.Combettes UPMC Universite Paris 06 Laboratoire Jacques-Louis Lions-UMR 7598 and Equipe Combinatoire et Optimisation-UMR 7090 UPMC Universite Paris 06 Laboratoire Jacques-Louis Lions-UMR 7598

A convex variational formulation is proposed to solve multicomponent signal processing problems in Hilbert *** cost function consists of a separable term, in which each component is modeled through its own potential,and of a coupling term, in which constraints on linear transformations of the components are penalized with smooth *** algorithm with guaranteed weak convergence to a solution to the problem is *** multicomponent signal decomposition and recovery applications are discussed.

关键词： Convex optimization denoising image restoration proximal algorithm signal decom-position signal recovery

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Two fast variance-reduced proximal gradient algorithms for SMVIPs-Stochastic Mixed Variational Inequality Problems with suitable applications to stochastic network games and traffic assignment problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2022年第0期408卷 114132-114132页

作者： Yang, Zhen-Ping Lin, Gui-Hua Jiaying Univ Sch Math Meizhou 514015 Guangdong Peoples R China Shanghai Univ Sch Management Shanghai 200444 Peoples R China

In this paper, we propose two proximal gradient algorithms with variance reduction for stochastic mixed variational inequality problems. One is a proximal extragradient algorithm and another is a proximal forward-backward-forward algorithm. Under the monotonicity assumption on the mapping F and other moderate conditions, we derive some asymptotic convergence properties and O(1/k) convergence rate in terms of the restricted gap function values for the proposed algorithms. Furthermore, under the bounded metric subregularity condition, we investigate the linear convergence rate and oracle complexity bounds for the proposed algorithms when the sample-size increases at a geometric rate. If the sample-size increases at a polynomial rate of [k+1](-s) with s > 0, the mean-squared distance of the iterates to the solution set decays at a corresponding polynomial rate, while the iterations and oracle complexities to obtain an epsilon-solution are O(1/epsilon(1/s)) and O(1/epsilon(1+1/s)) respectively. Finally, some numerical experiments on stochastic network games and traffic assignment problems indicate that the proposed algorithms are efficient. (c) 2022 Elsevier B.V. All rights reserved.

关键词： Nonlinear programming Stochastic mixed variational inequality Stochastic approximation proximal algorithm Variance reduction Complexity

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Distributed decision-coupled constrained optimization via proximal-Tracking

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AUTOMATICA 2022年 135卷 109938-109938页

作者： Falsone, Alessandro Prandini, Maria Politecn Milan Dipartimento Elettron Informaz & Bioingn Via Ponzio 34-5 I-20133 Milan Italy

In this paper we deal with decision-coupled problems involving multiple agents over a network. Each agent has its own local objective function and local constraints, and all agents aim at finding the value of a common decision vector that minimizes the sum of all agents' cost functions and satisfies all local constraints. To this purpose, we introduce a proximal-Tracking distributed optimization algorithm that integrates dynamic average consensus within the proximal minimization method. Convergence to an optimal consensus solution is guaranteed for any value of a constant penalty parameter, under a convexity assumption only, without requiring differentiability, Lipschitz continuity, or smoothness of the local objective functions. Numerical simulations show the effectiveness of the proposed scheme. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： \ Distributed optimization Decision-coupled optimization proximal algorithm Gradient-tracking

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A survey of sparse regularization based compression methods 8

A survey of sparse regularization based compression methods

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8th International Conference on Information Technology and Quantitative Management (ITQM) - Developing Global Digital Economy after COVID-19

作者： Tang, Anda Quan, Pei Niu, Lingfeng Shi, Yong Univ Chinese Acad Sci Sch Math Sci Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Econ & Management Beijing 100190 Peoples R China Univ Chinese Acad Sci Sch Comp Sci & Technol Beijing 100049 Peoples R China Chinese Acad Sci Res Ctr Fictitious Econ & Data Sci China 100190 Peoples R China Univ Nebraska Omaha Coll Informat Sci & Technol Omaha NE 68182 USA

In recent years, deep neural networks (DNNS) have attracted extensive attention due to their excellent performance in many fields of vision and speech recognition. With the increasing scale of tasks to be solved, the network used is becoming wider and deeper, which requires millions or even billions of parameters. The deep and wide network with many parameters brings the problems of memory requirement, computing overhead and over fitting, which seriously hinder the application of DNNS in practice. Therefore, a natural idea is to train sparse networks and floating-point operators with fewer parameters while maintaining considerable performance. In the past few years, a lot of researches have been put forward in the field of neural network compression, including sparse-inducing methods, quantization, knowledge distillation and so on. The sparse-inducing methods can be roughly divided into pruning, dropout and sparse regularization based optimization. In this paper, we briefly review and analyze the sparse regularization optimization methods. For the model and optimization method of sparse regularization based compression, we discuss both the different advantages and disadvantages. Finally, we provide some insights and discussion on how to make sparse regularization fit within the compression framework. (C) 2021 The Authors. Published by Elsevier B.V.

关键词： deep neural networks sparsity learning sparse regularizer proximal algorithm subgradient descent compression pruning

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Sparse Distortionless Beamformer Based on Nonconvex Optimization 29

Sparse Distortionless Beamformer Based on Nonconvex Optimiza...

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29th European Signal Processing Conference (EUSIPCO)

作者： Kawamura, Taiga Yatabe, Kohei Miyazaki, Ryoichi Natl Inst Technol Tokuyama Coll Yamaguchi Japan Waseda Univ Tokyo Japan

ISBN: (纸本)9789082797060

Minimum power distortionless response (MPDR) beamformer is a popular beamformer that minimizes its output power under the distortionless constraint. To improve the performance of the MPDR beamformer, a sparse distortionless beamformer has been proposed. It minimizes the l(1) norm of the output signal under the same constraint so that the output has sparse time-frequency representation. While the l(1)-norm-based formulation is theoretically advantageous owing to its convexity, its practical performance might not be excellent because of the bias of the l(1) norm. To reduce the bias and improve the performance, we propose a sparse distortionless beamformer based on a nonconvex sparsity-inducing objective function. The proposed beamformer is performed via a heuristic application of a primal-dual splitting algorithm. The experiments showed that the proposed beamformer can achieve higher performance and is more robust against mismatch of the target direction.

关键词： Microphone array speech enhancement sparse time-frequency representation proximal algorithm

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