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40th IEEE International Conference on Acoustics, Speech, and Signal Processing, ICASSP 2015

作者： Repetti, Audrey Chouzenoux, Emilie Pesquet, Jean-Christophe Université Paris-Est Lab. d'Informatique Gaspard Monge UMR CNRS 8049 Champs-sur-Marne Marne-la-Vallée France

ISBN: (纸本)9781467369978

primal-dual proximal optimization methods have recently gained much interest for dealing with very large-scale data sets encoutered in many application fields such as machine learning, computer vision and inverse problems [1-3]. In this work, we propose a novel random block-coordinate version of such algorithms allowing us to solve a wide array of convex variational problems. One of the main advantages of the proposed algorithm is its ability to solve composite problems involving large-size matrices without requiring any inversion. In addition, the almost sure convergence to an optimal solution to the problem is guaranteed. We illustrate the good performance of our method on a mesh denoising application. © 2015 IEEE.

关键词： block-coordinate algorithm convex optimization denoising inverse problems mesh processing nonsmooth optimization primal-dual algorithm proximity operator stochastic algorithm

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A novel distributed primal-dual control algorithm for energy management of DC microgrids considering network constraints

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2024年 155卷

作者： Shen, Jiaming Wang, Laili Zhu, Lei Xi An Jiao Tong Univ Elect Power Engn Dept Xian Peoples R China

A discrete-time control method is presented for real-time energy management of DC microgrids, where each distributed controller only shares information with its neighbors. Controllers aim to achieve economic dispatch and voltage restoration while maintaining the generator outputs and line currents in their allowable ranges. The proposed control method is developed based on a primal-dual algorithm (PDA) to determine the optimal control variables, in which uncoordinated step-sizes and an adaptive mechanism are introduced to accelerate the al-gorithm. The convergence analysis is also provided. Finally, numerical tests show the high convergence rate of the algorithm, and the hardware experiments demonstrate the applicability of the proposed control method for real-time energy management.

关键词： DC microgrids Distributed control Energy management primal-dual algorithm Consensus algorithm

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A random block-coordinate primal-dual proximal algorithm with application to 3D mesh denoising

A random block-coordinate primal-dual proximal algorithm wit...

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IEEE International Conference on Acoustics, Speech and Signal Processing

作者： A. Repetti E. Chouzenoux J. C. Pesquet Lab. d'Inf. Gaspard Monge Univ. Paris-Est Marne-la-Vallee France

ISBN: (纸本)9781467369985

关键词： block-coordinate algorithm convex optimization denoising inverse problems mesh processing nonsmooth optimization primal-dual algorithm proximity operator stochastic algorithm Noise reduction Inverse method Convex function Medical Subject Headings

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Convergence analysis of a primal-dual optimization-by-continuation algorithm

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2025年 457卷

作者： Loris, Ignace Rebegoldi, Simone Univ Libre Bruxellles Math Dept Blvd Triomphe B-1050 Brussels Belgium Univ Modena & Reggio Emilia Dipartimento Sci Fis Informat & Matemat Via Campi 213-B I-41125 Modena Italy

We present a numerical iterative optimization algorithm for the minimization of a cost function consisting of a linear combination of three convex terms, one of which is differentiable, a second one is prox-simple and the third one is the composition of a linear map and a proxsimple function. The algorithm's special feature lies in its ability to approximate, in a single iteration run, the minimizers of the cost function for many different values of the parameters determining the relative weight of the three terms in the cost function. A proof of convergence of the algorithm, based on an inexact variable metric approach, is also provided. As a special case, one recovers a generalization of the primal-dual algorithm of Chambolle and Pock, and also of the proximal-gradient algorithm. Finally, we show how it is related to a primal-dual iterative algorithm based on inexact proximal evaluations of the non-smooth terms of the cost function.

关键词： primal-dual algorithm Proximal algorithm Inverse problem Iterative algorithm

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Quasi-Newton Methods for Monotone Inclusions: Efficient Resolvent Calculus and primal-dual algorithms\ast

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SIAM JOURNAL ON IMAGING SCIENCES 2025年第1期18卷 308-344页

作者： Wang, Shida Fadili, Jalal Ochs, Peter Saarland Univ Dept Math & Comp Sci D-66123 Saarbrucken Saarland Germany Normandie Univ ENSICAEN CNRS GREYC F-14050 Caen France

We introduce two quasi-Newton forward-backward splitting algorithms to solve a class of monotone inclusion problems. The bottleneck is the evaluation of the resolvent operator. Changing the metric makes its computation even harder, and this is even true for a simple operator whose resolvent is known for the standard metric. To fully exploit the advantage of adapting the metric, we develop a new efficient resolvent calculus for a low-rank perturbed standard metric, which accounts exactly for quasi-Newton metrics. Moreover, we prove the convergence of our algorithms, including linear convergence rates in case one of the two considered operators is strongly monotone. As a by-product of our general monotone inclusion framework, we introduce two variants of the quasi-Newton primaldual hybrid gradient method (PDHG) for solving saddle point problems. The favorable performance of these two quasi-Newton PDHG methods is demonstrated on several numerical experiments in image processing.

关键词： quasi-Newton resolvent operator primal-dual algorithm

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Psychological modeling for community energy systems

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ENERGY REPORTS 2025年 13卷 2219-2229页

作者： Zhao, Alexis Pengfei Alhazmi, Mohannad Huo, Da Li, Wanzi Stanford Univ Stanford Doerr Sch Sustainabil Dept Energy Sci & Engn Stanford CA 94305 USA King Saud Univ Coll Appl Engn Elect Engn Dept POB 2454 Riyadh 11451 Saudi Arabia Cranfield Univ Energy Syst Intelligence Ctr Energy Syst & Strateg Cranfield MK43 0AL Beds England Cornell Univ Cornell Coll Human Ecol Ithaca NY 14853 USA

This paper introduces a novel framework for community energy system (CES) optimization that integrates Social Cognitive Theory (SCT) with Distributionally Robust Optimization (DRO) to address both behavioral and technical challenges. The rapid integration of renewable energy resources and the proliferation of peer-to-peer (P2P) trading platforms necessitate solutions that balance economic efficiency, environmental sustainability, and user engagement under uncertainty. While existing studies focus predominantly on technical optimization, they often neglect the significant influence of behavioral dynamics on community energy systems. This research bridges the gap by explicitly incorporating peer influence, observational learning, and engagement incentives into a robust optimization framework. The proposed methodology models user behavior through SCT, enabling dynamic adjustments to trading patterns and energy-sharing decisions. A DRO model is employed to handle uncertainties in renewable energy generation and demand, ensuring system reliability and resilience. To enhance computational efficiency, a primal-dual algorithm is developed, offering faster convergence compared to traditional DRO methods. The framework is validated through a comprehensive case study on a 50- household microgrid equipped with solar, wind, and storage systems, alongside a P2P trading platform. Results demonstrate the framework's ability to reduce carbon emissions by up to 30%, improve renewable energy utilization to over 90%, and increase trading participation by 25%, compared to baseline scenarios. This study makes four key contributions: (1) introducing SCT-based behavioral modeling to enhance user engagement in CES operations, (2) leveraging DRO to address uncertainties in renewable energy and demand profiles, (3) proposing a primal-dual algorithm for scalable and efficient optimization, and (4) presenting a unified framework that balances economic, environmental, and social objectives. The

关键词： Social Cognitive Theory Distributionally robust optimization Peer-to-peer trading Community energy systems Renewable energy integration Behavioral modeling primal-dual algorithm

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Distributed aggregative optimization with affine coupling constraints

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NEURAL NETWORKS 2025年 184卷 107085页

作者： Du, Kaixin Meng, Min Tongji Univ Shanghai Res Inst Intelligent Autonomous Syst Shanghai 201210 Peoples R China Tongji Univ Coll Elect & Informat Engn Dept Control Sci & Engn Shanghai 201804 Peoples R China Natl Key Lab Autonomous Intelligent Unmanned Syst Shanghai Peoples R China Minist Educ Frontiers Sci Ctr Intelligent Autonomous Syst Shanghai Peoples R China

This paper investigates a distributed aggregative optimization problem subject to coupling affine inequality constraints, in which local objective functions depend not only on their own decision variables but also on an aggregation of all the agents' variables. The formulated problem encompasses numerous practical applications, such as commodity distribution, electric vehicle charging, and energy consumption control in power grids. Hence, there is a compelling need to explore anew neurodynamic approach to address this. To this end, a novel distributed aggregative primal-dual algorithm is proposed based on the dual diffusion strategy and distributed tracking technique, which typically makes a slight yet important modification to the traditional primal-dual methods. Leveraging an elaborately constructed weighted error norm sum, it is rigorously proved that the devised algorithm converges to the optimal solution at a linear rate. Finally, numerical simulations are conducted to demonstrate the theoretical results and show the advantages of the proposed algorithm.

关键词： Distributed aggregative optimization Coupling affine inequality constraints primal-dual algorithm Linear convergence rate

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Lagrange-dual-based fully distributed economic dispatch in smart grids with transmission line losses

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ASIAN JOURNAL OF CONTROL 2025年第0期

作者： Lin, Luxin Chen, Zhiyi Wang, Xiangyu Li, Shihua Yu, Xinghuo Southeast Univ Sch Automat Key Lab Measurement & Control Complex Syst Engn Minist Educ Nanjing 210096 Peoples R China RMIT Univ Sch Engn Melbourne Vic Australia

Economic dispatch constitutes an important element within the hierarchical control framework of smart grids. Its effective implementation is imperative for cost reduction in generation, enhancement of operational efficiency, and power systems stability. This paper tackles the distributed economic dispatch problem in smart grids with transmission line losses. First, the economic dispatch problem is transformed into its Lagrange dual problem using convex optimization theory, accompanied by a description of the strategy for addressing inequality constraints. Then, a fully distributed optimization algorithm is developed under free initial state through the fusion of nonsmooth analysis and the primal-dual method. Furthermore, based on this algorithm, a modified algorithm with lower communication overhead is presented. Finally, software simulations and hardware-in-the-loop tests are performed to verify the developed scheme.

关键词： economic dispatch Lagrange dual problem primal-dual algorithm smart grids transmission line losses

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An Augmented Lagrangian primal-dual Semismooth Newton Method for Multi-Block Composite Optimization

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JOURNAL OF SCIENTIFIC COMPUTING 2025年第3期102卷 1-30页

作者： Deng, Zhanwang Deng, Kangkang Hu, Jiang Wen, Zaiwen Peking Univ Acad Adv Interdisciplinary Studies Beijing 100871 Peoples R China Natl Univ Def Technol Dept Math Changsha 410073 Peoples R China Univ Calif Berkeley Dept Math Berkeley CA 94720 USA Peking Univ Beijing Int Ctr Math Res Ctr Machine Learning Res Beijing 100871 Peoples R China Peking Univ Changsha Inst Comp & Digital Econ Beijing 100871 Peoples R China

In this paper, we develop a novel primal-dual semismooth Newton method for solving linearly constrained multi-block convex composite optimization problems. First, a differentiable augmented Lagrangian (AL) function is constructed by utilizing the Moreau envelopes of the nonsmooth functions. It enables us to derive an equivalent saddle point problem and establish the strong AL duality under the Slater's condition. Consequently, a semismooth system of nonlinear equations is formulated to characterize the optimality of the original problem instead of the inclusion-form KKT conditions. We then develop a semismooth Newton method, called ALPDSN, which uses purely second-order steps and a nonmonotone line search based globalization strategy. Through a connection to the inexact first-order steps when the regularization parameter is sufficiently large, the global convergence of ALPDSN is established. Under the partial smoothness, the local error bound, and the strict complementarity conditions, we show that both the primal and the dual iteration sequences possess a superlinear convergence rate and provide concrete examples where these regularity conditions are met. Numerical results demonstrate the high efficiency and robustness of the proposed ALPDSN.

关键词： Semismooth Newton method primal-dual algorithm Globalization Superlinear convergence

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A Second-Order TGV Discretization with 90° Rotational Invariance Property

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JOURNAL OF MATHEMATICAL IMAGING AND VISION 2025年第2期67卷 1-33页

作者： Hosseini, Alireza Bredies, Kristian Univ Tehran Coll Sci Sch Math Stat & Comp SciStat & Comp SciStat & Comp POB 14115-175 Tehran Iran Karl Franzens Univ Graz Dept Math & Sci Comp Heinrich str 36 A-8010 Graz Austria

In this work, we propose a new discretization for second-order total generalized variation (TGV) with some distinct properties compared to existing discrete formulations. The introduced model is based on the same design principles as Condat's discrete total variation model (Condat in SIAM J Imaging Sci 10(3):1258-1290, 2017) and shares its benefits, particularly improved solution quality for imaging problems. We propose an algorithm for general discrete inverse problems with second-order TGV using the new discretization. Numerical results obtained with this algorithm for denoising and upscaling demonstrate the advantages of the discretization. Moreover, to assess the invariance properties of the new model, we compare the results of the proposed TGV and the classic discrete TGV for original data and 90 degrees rotated versions. Additionally, we provide an algorithm for calculating the TGV value with respect to the new discretization model.

关键词： Image processing Total generalized variation TGV discretization Inverse problem primal-dual algorithm

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