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2016 IEEE International Conference on Signal and Image Processing

作者： Kaizhan Huai Yejun Li Mingfang Ni Zhanke Yu Xiaoguo Wang Institute of Communications Engineering PLA University of Science and Technology Xi'an Communications Institute

Compressive sensing(CS) is a new framework for simulations sensing and *** to reconstruct a sparse signal from limited measurements is the key problem in *** solving the reconstruction problem of a sparse signal, we proposed a self-adaptive proximal point algorithm(PPA).This algorithm can handle the sparse signal reconstruction by solving a substituted problem—l *** last, the numerical results shows that the proposed method is more effective compared with the compressive sampling matching pursuit(CoSaMP).

关键词： compressive sensing signal reconstruction proximal point algorithm self-adaptive

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Comments on "The proximal point algorithm Revisited"

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2015年第1期166卷 343-349页

作者： Dong, Yunda Zhengzhou Univ Sch Math & Stat Zhengzhou 450001 Peoples R China

Very recently, the author gave an upper bound on a decreasing positive sequence. And, he made use of it to improve a classical result of Br,zis and Lions concerning the proximal point algorithm for monotone inclusion in an infinite-dimensional Hilbert space. One assumption is the algorithm's strong convergence. In this paper, we derive a new upper bound on this decreasing positive sequence and thus achieve the same improvement without requiring this assumption.

关键词： Monotone inclusion Convex minimization proximal point algorithm Rate of convergence

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A proximal point algorithm for DC fuctions on Hadamard manifolds

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JOURNAL OF GLOBAL OPTIMIZATION 2015年第4期63卷 797-810页

作者： Souza, J. C. O. Oliveira, P. R. Univ Fed Rio de Janeiro COPPE Sistemas BR-21945970 Rio De Janeiro RJ Brazil Univ Fed Piaui CEAD Teresina PI Brazil

An extension of a proximal point algorithm for difference of two convex functions is presented in the context of Riemannian manifolds of nonposite sectional curvature. If the sequence generated by our algorithm is bounded it is proved that every cluster point is a critical point of the function (not necessarily convex) under consideration, even if minimizations are performed inexactly at each iteration. Application in maximization problems with constraints, within the framework of Hadamard manifolds is presented.

关键词： Nonconvex optimization proximal point algorithm DC functions Hadamard manifolds

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A fast proximal point algorithm for l₁-minimization problem in compressed sensing

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APPLIED MATHEMATICS AND COMPUTATION 2015年 270卷 777-784页

作者： Zhu, Yun Wu, Jian Yu, Gaohang Gannan Normal Univ Sch Phys & Elect Informat Ganzhou 341000 Peoples R China Harbin Inst Technol Shenzhen Grad Sch Sch Comp Sci & Technol Harbin Peoples R China Gannan Normal Univ Sch Math & Comp Sci Ganzhou 341000 Peoples R China

In this paper, a fast proximal point algorithm (PPA) is proposed for solving l(1)-minimization problem arising from compressed sensing. The proposed algorithm can be regarded as a new adaptive version of customized proximal point algorithm, which is based on a novel decomposition for the given nonsymmetric proximal matrix M. Since the proposed method is also a special case of the PPA-based contraction method, its global convergence can be established using the framework of a contraction method. Numerical results illustrate that the proposed algorithm outperforms some existing proximal point algorithms for sparse signal reconstruction. (C) 2015 Elsevier Inc. All rights reserved.

关键词： proximal point algorithm l(1)-regularized least square Compressed sensing

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Convergence of the generalized contraction-proximal point algorithm in a Hilbert space

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OPTIMIZATION 2015年第4期64卷 709-715页

作者： Wang, Fenghui Cui, Huanhuan Xi An Jiao Tong Univ Inst Informat & Syst Sci Xian Peoples R China Luoyang Normal Univ Dept Math Luoyang Peoples R China

We study the contraction-proximal point algorithm that has the following iterative form: where is a fixed element, is the resolvent operator and are all real sequences. The algorithm is known to converge strongly under the assumption that is bounded below away from zero and above away from 1. In this paper, we show that this condition can be further relaxed as

关键词： 47J20 90C25 49J40 65J15 firmly nonexpansive operator proximal point algorithm maximal monotone operator

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Variance Reduction Techniques for Stochastic proximal point algorithms

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2024年第2期203卷 1910-1939页

作者： Traore, Cheik Apidopoulos, Vassilis Salzo, Saverio Villa, Silvia Univ Genoa Malga Ctr DIMA Genoa Italy Univ Genoa Malga Ctr Dibris Genoa Italy Sapienza Univ Roma Rome Italy

In the context of finite sums minimization, variance reduction techniques are widely used to improve the performance of state-of-the-art stochastic gradient methods. Their practical impact is clear, as well as their theoretical properties. Stochastic proximal point algorithms have been studied as an alternative to stochastic gradient algorithms since they are more stable with respect to the choice of the step size. However, their variance-reduced versions are not as well studied as the gradient ones. In this work, we propose the first unified study of variance reduction techniques for stochastic proximal point algorithms. We introduce a generic stochastic proximal-based algorithm that can be specified to give the proximal version of SVRG, SAGA, and some of their variants. For this algorithm, in the smooth setting, we provide several convergence rates for the iterates and the objective function values, which are faster than those of the vanilla stochastic proximal point algorithm. More specifically, for convex functions, we prove a sublinear convergence rate of O(1/k). In addition, under the Polyak-& lstrok;ojasiewicz condition, we obtain linear convergence rates. Finally, our numerical experiments demonstrate the advantages of the proximal variance reduction methods over their gradient counterparts in terms of the stability with respect to the choice of the step size in most cases, especially for difficult problems.

关键词： Stochastic optimization proximal point algorithm Variance reduction techniques SVRG SAGA

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Weak and strong convergence of generalized proximal point algorithms with relaxed parameters

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JOURNAL OF GLOBAL OPTIMIZATION 2023年第4期85卷 969-1002页

作者： Hui Ouyang Univ British Columbia Math Kelowna BC V1V 1V7 Canada

In this work, we propose and study a framework of generalized proximal point algorithms associated with a maximally monotone operator. We indicate sufficient conditions on the regularization and relaxation parameters of generalized proximal point algorithms for the equivalence of the boundedness of the sequence of iterations generated by this algorithm and the non-emptiness of the zero set of the maximally monotone operator, and for the weak and strong convergence of the algorithm. Our results cover or improve many results on generalized proximal point algorithms in our references. Improvements of our results are illustrated by comparing our results with related known ones.

关键词： proximal point algorithm Maximally monotone operators Resolvent Firmly nonexpansiveness Weak convergence Strong convergence

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Approximate Customized proximal point algorithms for Separable Convex Optimization

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Journal of the Operations Research Society of China 2023年第2期11卷 383-408页

作者： Hong-Mei Chen Xing-Ju Cai Ling-Ling Xu School of Mathematical Sciences Nanjing Normal UniversityNanjing 210023JiangsuChina Jiangsu Key Laboratory for NSLSCS Nanjing Normal UniversityNanjing 210023JiangsuChina

proximal point algorithm(PPA)is a useful algorithm framework and has good convergence *** difficulty is that the subproblems usually only have iterative *** this paper,we propose an inexact customized PPA framework for twoblock separable convex optimization problem with linear *** design two types of inexact error criteria for the *** first one is absolutely summable error criterion,under which both subproblems can be solved *** one of the two subproblems is easily solved,we propose another novel error criterion which is easier to implement,namely relative error *** relative error criterion only involves one parameter,which is more *** establish the global convergence and sub-linear convergence rate in ergodic sense for the proposed *** numerical experiments on LASSO regression problems and total variation-based image denoising problem illustrate that our new algorithms outperform the corresponding exact algorithms.

关键词： Inexact criteria proximal point algorithm Alternating direction method of multipliers Separable convex programming

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proximal point algorithms based onS-iterative technique for nearly asymptotically quasi-nonexpansive mappings and applications

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NUMERICAL algorithmS 2021年第4期86卷 1561-1590页

作者： Sahu, D. R. Kumar, Ajeet Kang, Shin Min Banaras Hindu Univ Inst Sci Dept Math Varanasi 221005 Uttar Pradesh India Gyeongsang Natl Univ Dept Math Jinju 52828 South Korea China Med Univ Ctr Gen Educ Taichung 40402 Taiwan

In this paper, we combine theS-iteration process introduced by Agarwal et al. (J. Nonlinear Convex Anal.,8(1), 61-792007) with the proximal point algorithm introduced by Rockafellar (SIAM J. Control Optim.,14, 877-8981976) to propose a new modified proximal point algorithm based on theS-type iteration process for approximating a common element of the set of solutions of convex minimization problems and the set of fixed points of nearly asymptotically quasi-nonexpansive mappings in the framework of CAT(0) spaces and prove the o-convergence of the proposed algorithm for solving common minimization problem and common fixed point problem. Our result generalizes, extends and unifies the corresponding results of Dhompongsa and Panyanak (Comput. Math. Appl.,56, 2572-25792008), Khan and Abbas (Comput. Math. Appl.,61, 109-1162011), Abbas et al. (Math. Comput. Modelling,55, 1418-14272012) and many more.

关键词： Convex minimization problem Fixed point problem Nearly asymptotically quasi-nonexpansive mapping Mean nonexpansive mapping S-iteration process proximal point algorithm CAT(0) space o-convergence

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Entropy-Like Minimization Methods Based On Modified proximal point algorithm

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INFOR 2014年第3期52卷 147-156页

作者： Hamdi, Abdelouahed Bnouhachem, Abdellah Qatar Univ Dept Math Stat & Phys Doha Qatar Nanjing Univ Sch Management Sci & Engn Nanjing 210093 Jiangsu Peoples R China Ibn Zohr Univ ENSA Agadir Morocco

In this paper we introduce an extension of the proximal point algorithm proposed by Guler for solving convex minimization problems. This extension is obtained by substituting the usual quadratic proximal term by a class of convex nonquadratic entropy-like distances, called phi-divergences. A study of the convergence rate of this new proximal point method under mild assumptions is given, and further it is shown that this estimate rate is better than the available one of proximal-like methods. Some applications are given concerning general convex minimizations, linearly constrained convex programs and variationnal inequalities.

关键词： proximal point algorithm interior proximal methods nonquadratic regularizations variationnal inequalities

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