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dual algorithm for truncated fractional variation based image denoising

INTERNATIONAL JOURNAL OF COMPUTER MATHEMATICS 2020年第9期97卷 1849-1859页

作者： Liang, Haixia Zhang, Juli Xian Jiaotong Liverpool Univ Dept Math Sci 111 Renai RdSuzhou Ind Pk Suzhou Jiangsu Peoples R China Shanghai Univ Engn Sci Sch Math Phys & Stat Shanghai Peoples R China

Fractional-order derivative is attracting more and more attention of researchers in image processing because of its better property in restoring more texture than the total variation. To improve the performance of fractional-order variation model in image restoration, a truncated fractional-order variation model was proposed in Chan and Liang [Truncated fractional-order variation model for image restoration, J. Oper. Res. Soc. China]. In this paper, we propose a dual approach to solve this truncated fractional-order variation model on noise removal. The proposed algorithm is based on the dual approach proposed by Chambolle [An algorithm for total variation minimisation and applications, J. Math Imaging Vis. 20 (2004), pp. 89-97]. Conversely, the Chambolle's dual approach can be treated as a special case of the proposed algorithm with fractional order . The work of this paper modifies the result in Zhang et al. [Adaptive fractional-order multi-scale method for image denoising, J. Math. Imaging Vis. 43(1) (2012), pp. 39-49. Springer Netherlands 0924-9907, Computer Science, pp. 1-11, 2011], where the convergence is not analysed. Based on the truncation, the convergence of the proposed dual method can be analysed and the convergence criteria can be provided. In addition, the accuracy of the reconstruction is improved after the truncation is taken.

关键词： Truncated fractional-order derivative truncated fractional-order variation model dual algorithm image denoising texture preserving

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A dual algorithm for the topology optimization of non-linear elastic structures

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING 2009年第4期77卷 502-517页

作者： Jog, C. S. Indian Inst Sci Dept Mech Engn Bangalore 560012 Karnataka India

dual algorithms are ideally suited for the purpose of topology optimization since they work in the space of Lagrange multipliers associated with the constraints. To date, dual algorithms have been applied only for linear structures. Here we extend this methodology to the case of non-linear structures. The perimeter constraint is used to make the topology problem well-posed. We show that the proposed algorithm yields a value of perimeter that is close to that specified by the user. We also address the issue of manufacturability of these designs, by proposing a variant of the standard dual algorithm, which generates designs that are two-dimensional although the loading and the geometry are three-dimensional. Copyright (C) 2008 John Wiley & Sons, Ltd.

关键词： dual algorithm non-linear topology optimization

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Linearisation techniques and the dual algorithm for a class of mixed singular/continuous control problems in reinsurance. Part II: Numerical aspects

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APPLIED MATHEMATICS AND COMPUTATION 2024年 473卷

作者： Goreac, Dan Li, Juan Wang, Pangbo Xu, Boxiang Shandong Univ Weihai Sch Math & Stat Weihai 264209 Peoples R China Univ Laval Ecole Actuariat Quebec City PQ Canada Univ Gustave Eiffel Univ Paris Est Creteil LAMAUPEM CNRS F-77447 Marne La Vallee France Shandong Univ Res Ctr Math & Interdisciplinary Sci Qingdao 266237 Peoples R China Shandong Univ Zhongtai Secur Inst Financial Studies Jinan 250100 Peoples R China

This paper is intended as a companion to [12] and focuses on the numerical implementations of the method in the context of insurance problems with mixed controls: reinsurance acting as continuous control, and capital injection and dividend payment acting as singular ones. The aim is twofold. On the one hand, we provide a comparison of the output of our method in terms of the optimal value against two benchmarks. The first benchmark is provided by [4] in the noreinsurance setting and when the claims are exponentially distributed. The second benchmark refers to [8] where capital injections are not permitted, but different claim distributions can be employed. On the other hand, we illustrate the improvement of the models in [8] when capital injection is allowed. We also look into the effect of reinsurance in the model [4]. Several cases for the equity cost parameter are discussed as are the boundary (or limit) situations.

关键词： Singular/continuous control Linear programming dual algorithm Reinsurance Capital injection Dividends Occupation measure dual dynamic programming

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A global and local active contour model based on dual algorithm for image segmentation

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COMPUTERS & MATHEMATICS WITH APPLICATIONS 2017年第6期74卷 1471-1488页

作者： Xu, Haiyong Jiang, Gangyi Yu, Mei Luo, Ting Ningbo Univ Coll Sci & Technol Ningbo 315211 Zhejiang Peoples R China Ningbo Univ Fac Informat Sci & Engn Ningbo 315211 Zhejiang Peoples R China Nanjing Univ State Key Lab Novel Software Technol Nanjing 210093 Jiangsu Peoples R China

Most of local region-based active contour models in terms of the level set approach are able to segment images with intensity inhomogeneity. However, these models do not utilize global statistical information and are quite sensitive to the initial placement of the contour. This paper presents a new global and local region-based active contour model to segment images with intensity inhomogeneity. First, in order to reduce number of iterations, the global energy functional of the Chan-Vese (C-V) model is used as the global term. Then, the local term is proposed to incorporate both local spatial information and local intensity information to handle intensity inhomogeneity. Moreover, to increase robustness of the initialization of the contour and reduce number of iterations, a convex energy functional and the dual algorithm are designed in the numerical implementation. Experimental results for synthetic and medical images have shown the efficiency and robustness of the proposed method. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Image segmentation Active contour Level set Intensity inhomogeneity dual algorithm

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A dual algorithm for minimization of the LLT model

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ADVANCES IN COMPUTATIONAL MATHEMATICS 2009年第1-3期31卷 115-130页

作者： Chen, Hua-zhu Song, Jin-ping Tai, Xue-Cheng Univ Bergen Dept Math N-5009 Bergen Norway Henan Univ Inst Math Kaifeng 475004 Peoples R China Henan Univ Coll Math & Informat Sci Kaifeng 475004 Peoples R China

We apply the dual algorithm of Chambolle for the minimization of the LLT model. A convergence theorem is given for the proposed algorithm. The algorithm overcomes the numerical difficulties related to the non-differentiability of the LLT model. The dual algorithm is faster than the original gradient descent algorithm. Numerical experiments are supplied to demonstrate the efficiency of the algorithm.

关键词： Legendre-Fenchel transform dual algorithm Convergence analysis

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A dual algorithm FOR MINIMAX PROBLEMS

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2005年第1-2期17卷 401-418页

作者： He, Suxiang Wuhan Univ Technol Sch Sci Wuhan 430070 Peoples R China

In this paper, a dual algorithm, based on a smoothing function of Bertsekas (1982), is established for solving unconstrained minimax problems. It is proven that a sequence of points, generated by solving a sequence of unconstrained minimizers of the smoothing function with changing parameter t, converges with Q-superlinear rate to a Kuhn-Tucker point locally under some mild conditions. The relationship between the condition number of the Hessian matrix of the smoothing function and the parameter is studied, which also validates the convergence theory. Finally the numerical results are reported to show the effectiveness of this algorithm.

关键词： Minimax problem smoothing function dual algorithm condition number Q-superlinear rate

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The dual algorithm based on a class of nonlinear Lagrangians for nonlinear programming

The dual algorithm based on a class of nonlinear Lagrangians...

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6th World Congress on Intelligent Control and Automation

作者： Ren, Yong-Hong Zhang, Li-Wei Dalian Univ Technol Dept Appl Math Dalian Liaoning Provin Peoples R China

ISBN: (纸本)1424403316

This paper studies the properties of a class of nonlinear Lagrangians for nonlinear programming with inequality constraints. It's shown that under a set of conditions this class of Lagrange algorithm is locally convergent when the penalty parameter is larger than a threshold. An error bound estimate of the solution, depending on the penalty, is also established. The paper also discusses the properties of the dual function associated with the proposed nonlinear Lagrangians. Finally, the dual algorithm corresponding to the proposed nonlinear Lagrangians is developed and used to solve some numerical examples by using the nonlinear Lagrangians in the literature. Numerical results suggest that the dual algorithm is effective for solving nonlinear programming.

关键词： nonlinear programming nonlinear Lagrangian dual function dual algorithm

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Linearisation Techniques and the dual algorithm for a Class of Mixed Singular/Continuous Control Problems in Reinsurance. Part I: Theoretical Aspects *

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APPLIED MATHEMATICS AND COMPUTATION 2022年 431卷

作者： Goreac, Dan Li, Juan Xu, Boxiang Shandong Univ Sch Math & Stat Weihai 264209 Peoples R China Univ Gustave Eiffel Univ Paris Est Creteil UPEM LAMACNRS F-77447 Marne La Vallee France Shandong Univ Res Ctr Math & Interdisciplinary Sci Qingdao 266237 Peoples R China

This paper focuses on linearisation techniques for a class of mixed singular/continuous control problems and ensuing algorithms. The motivation comes from (re)insurance problems with reserve-dependent premiums with Cramer-Lundberg claims, by allowing singular dividend payments and capital injections. Using variational techniques and embedding the trajectories in an appropriate family of occupation measures, we provide the linearisation of such problems in which the continuous control is given by reinsurance policies and the singular one by dividends and capital injections. The linearisation translates into a dual dynamic programming (DDP) algorithm. An important part of the paper is dedicated to structural considerations allowing reasonable implementation. We also hint connections to methods relying on moment sum of squares and LMI (linear matrix inequality)-relaxations to approximate the optimal candidates.

关键词： Singular continuous control linear programming occupation measure dual dynamic programming dual algorithm

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Novel closed-loop dual control algorithm for solar trackers of parabolic trough collector systems

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SOLAR ENERGY 2023年第1期259卷 381-390页

作者： Saldivar-Aguilera, Tonathiu Q. Valentin-Coronado, Luis M. Pena-Cruz, Manuel I. Diaz-Ponce, Arturo Dena-Aguilar, Jose A. PICYT Ctr Invest Opt AC Unidad Aguascalientes Prol Constituc 607 Fracc Reserva Loma Bonita Aguascalientes 20200 Aguascalientes Mexico CONACYT Ctr Invest Opt AC Unidad Aguascalientes Prol Constituc 607 Fracc Reserva Loma Bonita Aguascalientes 20200 Aguascalientes Mexico Tecnol Nacl Mexico IT Pabellon De Arteaga Engn Dept Pabellon De Arteaga 20670 AGS Mexico

Parabolic trough systems require accurate, reliable, and robust solar trackers to achieve their maximum thermal efficiency. This paper presents a dual closed-loop control strategy for single-axis solar trackers of parabolic trough systems. This strategy consists of the use of a dual control feedback through the integration of a typical photodiode-based solar sensors, to perform the coarse control, and a proposed shadow-based visual device that performs the fine position adjustment. A comparative analysis between a simple closed-loop control, typically used in parabolic trough systems, and the proposed control algorithm was conducted. Experimental tests were carried out for several days under different weather conditions. The experimental results showed that the mean solar tracking error obtained with the simple control was 0.97 degrees, while the error of the proposed dual control was 0.21 degrees;i.e., the error decreased by 78%, demonstrating greater stability and robustness of solar tracking. The proposed strategy proved to be a technically and economically feasible option to increase accuracy, reliability, and robustness in single-axis solar tracking systems of parabolic trough systems.

关键词： Solar tracker dual algorithm Closed-loop control Parabolic trough collector

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A dual projective pivot algorithm for linear programming

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2004年第3期29卷 333-346页

作者： Pan, PQ SE Univ Dept Math Nanjing 210018 Peoples R China

Recently, a linear programming problem solver, called dual projective simplex method, was proposed (Pan, Computers and Mathematics with Applications, vol. 35, no. 6, pp. 119-135, 1998). This algorithm requires a crash procedure to provide an initial (normal or deficient) basis. In this paper, it is recast in a more compact form so that it can get itself started from scratch with any dual (basic or nonbasic) feasible solution. A new dual Phase-1 approach for producing such a solution is proposed. Reported are also computational results obtained with a set of standard NETLIB problems.

关键词： linear programming dual algorithm pseudo-basis pivot projection

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