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第41届中国控制会议

作者： Shaolei Lu Yue Wei Yulong Ding Jinqiang Cui Hao Fang Intelligent Collaborative Equipment Center Information Science Academy of China Electronics Technology Group Corporation Department of Mathematics and Theories Peng Cheng Laboratory Beijing Institute of Technology

ISBN: (数字)9789887581536

ISBN: (纸本)9781665482561

Distributed nonsmooth consensus optimization problems with the coupled inequality constraint are investigated in this *** global objective consists of convex and nonsmooth local cost *** agent has only the information of its corresponding local cost ***,the coupled inequality constraint and consensus constraint are also *** employing the proximal method,a distributed proximal-gradient algorithm is *** convergence result is theoretically analysed by using Lyapunov stability *** shows that the multi-agent system driven by the proposed algorithm can reach consensus and satisfy the coupled equality constraint at the optimal *** the end,the results of the simulation show the efficiency of the proposed algorithm.

关键词： Distributed Optimization Coupled Inequality Constraint proximal algorithm

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An Efficient Waveform Design Method with Spectral Coexistence and Pulse-like Autocorrelation Function

An Efficient Waveform Design Method with Spectral Coexistenc...

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IEEE Radar Conference (RadarConf)

作者： Zhang, Cut Pei, Jifang Zhang, Yujie Zhang, Yin Huo, Weibo Huang, Yulin Yang, Jianyu Univ Elect Sci & Technol China Sch Informat & Commun Engn Chengdu 611731 Peoples R China

ISBN: (纸本)9798350329216;9798350329209

Spectrum coexistence capability is particularly important for radar systems in complex electromagnetic environments, since it can suppress interference arising from signals in the common frequency band. In this paper, a unimodular waveform design method based on the Karush-Kuhn-Tucker (KKT) conditions is proposed to design transmit waveforms with spectral coexistence and pulse-like autocorrelation function. First, we construct the joint optimization problem as a stopband minimization problem subject to energy spectral density (ESD) and amplitude constraints. Subsequently, the constructed optimization problem is decomposed into multiple subproblems with a single constraint. In particular, we solve the coupling variables by analyzing the KKT conditions for the coupling subproblem. The proposed method achieves simultaneous optimization of spectral coexistence and pulse-like autocorrelation by constructing a new optimization framework and introducing a proximal algorithm, which also reduces the computational complexity and improves the efficiency of waveform design. Numerical simulation results demonstrate the effectiveness of the proposed method in terms of runtime and waveform characteristics.

关键词： Unimodular waveform spectral coexistence autocorrelation joint optimization proximal algorithm

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Nonsmooth Resource Allocation of Multiagent Systems With Disturbances: A proximal Approach

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IEEE TRANSACTIONS ON CONTROL OF NETWORK SYSTEMS 2021年第3期8卷 1454-1464页

作者： Zhu, Yanan Wen, Guanghui Yu, Wenwu Yu, Xinghuo Nanjing Univ Informat Sci & Technol Sch Automat Nanjing 210044 Peoples R China Southeast Univ Sch Math Jiangsu Prov Key Lab Networked Collect Intelligen Nanjing 210096 Peoples R China RMIT Univ Sch Engn Melbourne Vic 3001 Australia

This article aims to solve the nonsmooth resource allocation problem in the presence of a global network resource constraint and local set constraints in the framework of multiagent system optimization. It is assumed that multiagent systems are subject to some external disturbances, and the control inputs of the agents satisfy Lispchitz continuity. These two distinguished features render the existing distributed optimization algorithms, especially the subgradient-based algorithms inapplicable due to the employment of discontinuity of subgradients. To solve such a challenging resource allocation problem, a new kind of continuous-time proximal algorithm is designed with the aid of convex optimization theory and the internal-model technique. The proximal algorithm is further augmented by introducing an event-based communication scheme such that the continuous-time communication among the agents is avoided successfully. The theoretical analysis shows that the multiagent systems under the proposed algorithms can converge to the optimal solution of the considered problem, while the external disturbances are rejected. Besides, the Zeno behavior can be excluded for the proximal algorithm with event-based communication. Finally, the numerical simulations are given to verify the established theoretical results.

关键词： Disturbance rejection event-based communication multiagent systems proximal algorithm resource allocation

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Accelerated proximal Subsampled Newton Method

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2021年第10期32卷 4374-4388页

作者： Ye, Haishan Luo, Luo Zhang, Zhihua Chinese Univ Hong Kong Shenzhen Res Inst Big Data Shenzhen 518172 Peoples R China Hong Kong Univ Sci & Technol Dept Math Hong Kong Peoples R China Peking Univ Dept Math Beijing 100871 Peoples R China

Composite function optimization problem often arises in machine learning known as regularized empirical minimization. We introduce the acceleration technique to the Newton-type proximal method and propose a novel algorithm called accelerated proximal subsampled Newton method (APSSN). APSSN only subsamples a small subset of samples to construct an approximate Hessian that achieves computational efficiency. At the same time, APSSN still keeps a fast convergence rate. Furthermore, we obtain the scaled proximal mapping by solving its dual problem using the semismooth Newton method instead of resorting to the first-order methods. Due to our sampling strategy and the fast convergence rate of the semismooth Newton method, we can get the scaled proximal mapping efficiently. Both our theoretical analysis and empirical study show that APSSN is an effective and computationally efficient algorithm for composite function optimization problems.

关键词： Convergence Acceleration Approximation algorithms Newton method Optimization Machine learning Stochastic processes Approximate Newton Nesterov's acceleration nonsmooth optimization proximal algorithm

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Low-rank Tensor Learning with Nonconvex Overlapped Nuclear Norm Regularization

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JOURNAL OF MACHINE LEARNING RESEARCH 2022年第1期23卷 1-60页

作者： Yao, Quanming Wang, Yaqing Han, Bo Kwok, James T. Tsinghua Univ Dept Elect Engn Beijing Peoples R China Baidu Inc Baidu Res Beijing Peoples R China Hong Kong Baptist Univ Dept Comp Sci Hong Kong Peoples R China Hong Kong Univ Sci & Technol Dept Comp Sci & Engn Hong Kong Peoples R China

Nonconvex regularization has been popularly used in low-rank matrix learning. However, extending it for low-rank tensor learning is still computationally expensive. To address this problem, we develop an efficient solver for use with a nonconvex extension of the overlapped nuclear norm regularizer. Based on the proximal average algorithm, the proposed algorithm can avoid expensive tensor folding/unfolding operations. A special "sparse plus low-rank" structure is maintained throughout the iterations, and allows fast computation of the individual proximal steps. Empirical convergence is further improved with the use of adaptive momentum. We provide convergence guarantees to critical points on smooth losses and also on objectives satisfying the KurdykaLojasiewicz condition. While the optimization problem is nonconvex and nonsmooth, we show that its critical points still have good statistical performance on the tensor completion problem. Experiments on various synthetic and real-world data sets show that the proposed algorithm is efficient in both time and space and more accurate than the existing state-of-the-art.

关键词： Low-rank tensor proximal algorithm proximal average algorithm Nonconvex regu-larization Overlapped nuclear norm

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Alternative Design of DeepPDNet in the Context of Image Restoration

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IEEE SIGNAL PROCESSING LETTERS 2022年 29卷 932-936页

作者： Jiu, Mingyuan Pustelnik, Nelly Zhengzhou Univ Sch Comp & Artificial Intelligence Zhengzhou 450001 Peoples R China Univ Lyon 1 Univ Lyon ENS Lyon CNRSLab Phys F-69342 Lyon France UCLouvain ISPGrp ICTEAM B-1348 Louvain Belgium

This work designs an image restoration deep network relying on unfolded Chambolle-Pock primal-dual iterations. Each layer of our network is built from Chambolle-Pock iterations when specified for minimizing a sum of a l(2)-norm data-term and an analysis sparse prior. The parameters of our network are the step-sizes of the Chambolle-Pock scheme and the linear operator involved in sparsity-based penalization, including implicitly the regularization parameter. A backpropagation procedure is fully described. Preliminary experiments illustrate the good behavior of such a deep primal-dual network in the context of image restoration on BSD68 database.

关键词： Image restoration deep learning proximal algorithm Chambolle-Pock algorithm sparsity

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proximal algorithms and temporal difference methods for solving fixed point problems

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2018年第3期70卷 709-736页

作者： Bertsekas, Dimitri P. MIT Dept Elect Engn & Comp Sci Lab Informat & Decis Syst Cambridge MA 02139 USA

In this paper we consider large fixed point problems and solution with proximal algorithms. We show that for linear problems there is a close connection between proximal iterations, which are prominent in numerical analysis and optimization, and multistep methods of the temporal difference type such as TD(), LSTD(), and LSPE(), which are central in simulation-based exact and approximate dynamic programming. One benefit of this connection is a new and simple way to accelerate the standard proximal algorithm by extrapolation towards a multistep iteration, which generically has a faster convergence rate. Another benefit is the potential for integration into the proximal algorithmic context of several new ideas that have emerged in the approximate dynamic programming context, including simulation-based implementations. Conversely, the analytical and algorithmic insights from proximal algorithms can be brought to bear on the analysis and the enhancement of temporal difference methods. We also generalize our linear case result to nonlinear problems that involve a contractive mapping, thus providing guaranteed and potentially substantial acceleration of the proximal and forward backward splitting algorithms at no extra cost. Moreover, under certain monotonicity assumptions, we extend the connection with temporal difference methods to nonlinear problems through a linearization approach.

关键词： proximal algorithm Temporal differences Dynamic programming Convex optimization Fixed point problems

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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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Regression Models for Compositional Data: General Log-Contrast Formulations, proximal Optimization, and Microbiome Data Applications

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STATISTICS IN BIOSCIENCES 2021年第2期13卷 217-242页

作者： Combettes, Patrick L. Mueller, Christian L. North Carolina State Univ Dept Math Raleigh NC 27695 USA Flatiron Inst Ctr Computat Math New York NY 10010 USA Helmholtz Zentrum Munchen Inst Computat Biol Neuherberg Germany Ludwig Maxmilians Univ Munchen Dept Stat Munich Germany

Compositional data sets are ubiquitous in science, including geology, ecology, and microbiology. In microbiome research, compositional data primarily arise from high-throughput sequence-based profiling experiments. These data comprise microbial compositions in their natural habitat and are often paired with covariate measurements that characterize physicochemical habitat properties or the physiology of the host. Inferring parsimonious statistical associations between microbial compositions and habitat- or host-specific covariate data is an important step in exploratory data analysis. A standard statistical model linking compositional covariates to continuous outcomes is the linear log-contrast model. This model describes the response as a linear combination of log-ratios of the original compositions and has been extended to the high-dimensional setting via regularization. In this contribution, we propose a general convex optimization model for linear log-contrast regression which includes many previous proposals as special cases. We introduce a proximal algorithm that solves the resulting constrained optimization problem exactly with rigorous convergence guarantees. We illustrate the versatility of our approach by investigating the performance of several model instances on soil and gut microbiome data analysis tasks.

关键词： Compositional data Convex optimization Log-contrast model Microbiome Perspective function proximal algorithm

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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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