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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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dual algorithm for truncated fractional variation based image denoising

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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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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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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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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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Perturbed Utility Stochastic Traffic Assignment

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TRANSPORTATION SCIENCE 2024年第4期58卷 876页

作者： Yao, Rui Fosgerau, Mogens Paulsen, Mads Rasmussen, Thomas Kjaer Ecole Polytech Fed Lausanne Sch Architecture Civil & Environm Engn CH-1015 Lausanne Switzerland Univ Copenhagen Dept Econ DK-1353 Copenhagen Denmark Tech Univ Denmark Dept Technol Management & Econ DK-2800 Lyngby Denmark

This paper develops a fast algorithm for computing the equilibrium assignment with the perturbed utility route choice (PURC) model. Without compromise, this allows the significant advantages of the PURC model to be used in large-scale applications. We formulate the PURC equilibrium assignment problem as a convex minimization problem and find a closed -form stochastic network loading expression that allows us to formulate the Lagrangian dual of the assignment problem as an unconstrained optimization problem. To solve this dual problem, we formulate a quasi -Newton accelerated gradient descent algorithm (qN-AGD*). Our numerical evidence shows that qN-AGD* clearly outperforms a conventional primal algorithm and a plain accelerated gradient descent algorithm. qN-AGD* is fast with a runtime that scales about linearly with the problem size, indicating that solving the perturbed utility assignment problem is feasible also with very large networks.

关键词： perturbed utility stochastic traffic assignment dual algorithm closed-form network loading network route choice

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Reliability estimation and statistical inference under joint progressively Type-II right-censored sampling for certain lifetime distributions

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COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 2024年

作者： Lin, Chien-Tai Chen, Yen-Chou Yeh, Tzu-Chi Ng, Hon Keung Tony Tamkang Univ Dept Math New Taipei City Taiwan Bentley Univ Dept Math Sci Waltham MA USA

In this article, the parameter estimation of several commonly used two-parameter lifetime distributions, including the Weibull, inverse Gaussian, and Birnbaum-Saunders distributions, based on joint progressively Type-II right-censored sample is studied. Different numerical methods and algorithms are used to compute the maximum likelihood estimates of the unknown model parameters. These methods include the Newton-Raphson method, the stochastic expectation-maximization (SEM) algorithm, and the dual annealing (DA) algorithm. These estimation methods are compared in terms of accuracy (e.g. the bias and mean squared error), computational time and effort (e.g. the required number of iterations), the ability to obtain the largest value of the likelihood, and convergence issues by means of a Monte Carlo simulation study. Recommendations are made based on the simulated results. A real data set is analyzed for illustrative purposes. These methods are implemented in Python, and the computer programs are available from the authors upon request.

关键词： dual algorithm Maximum likelihood estimation Monte Carlo simulation Simulated annealing algorithm Stochastic EM algorithm

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Voting-Based Multiagent Reinforcement Learning for Intelligent IoT

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IEEE INTERNET OF THINGS JOURNAL 2021年第4期8卷 2681-2693页

作者： Xu, Yue Deng, Zengde Wang, Mengdi Xu, Wenjun So, Anthony Man-Cho Cui, Shuguang Beijing Univ Posts & Telecommun Minist Educ Key Lab Universal Wireless Commun Beijing 100876 Peoples R China Chinese Univ Hong Kong Shenzhen Res Inst Big Data Shenzhen 518172 Peoples R China Chinese Univ Hong Kong Sch Sci & Engn Shenzhen 518172 Peoples R China Chinese Univ Hong Kong Dept Syst Engn & Engn Management Hong Kong Peoples R China Princeton Univ Dept Elect Engn Ctr Stat & Machine Learning Dept Operat Res & Financial Engn Princeton NJ 08544 USA Princeton Univ Dept Comp Sci Princeton NJ 08544 USA Chinese Univ Hong Kong Future Network Intelligence Inst Shenzhen 518172 Peoples R China

The recent success of single-agent reinforcement learning (RL) in Internet of Things (IoT) systems motivates the study of multiagent RL (MARL), which is more challenging but more useful in large-scale IoT. In this article, we consider a voting-based MARL problem, in which the agents vote to make group decisions and the goal is to maximize the globally averaged returns. To this end, we formulate the MARL problem based on the linear programming form of the policy optimization problem and propose a primal-dual algorithm to obtain the optimal solution. We also propose a voting mechanism through which the distributed learning achieves the same sublinear convergence rate as centralized learning. In other words, the distributed decision making does not slow down the process of achieving global consensus on optimality. Finally, we verify the convergence of our proposed algorithm with numerical simulations and conduct case studies in practical multiagent IoT systems.

关键词： Convergence Internet of Things Optimization Collaboration Task analysis Learning (artificial intelligence) Games Multiagent reinforcement learning (MARL) primal– dual algorithm voting mechanism

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Deformable Image Registration Based on Functions of Bounded Generalized Deformation

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INTERNATIONAL JOURNAL OF COMPUTER VISION 2021年第5期129卷 1341-1358页

作者： Nie, Ziwei Li, Chen Liu, Hairong Yang, Xiaoping Nanjing Univ Dept Math Nanjing 210093 Peoples R China Nanjing Forestry Univ Sch Sci Nanjing 210037 Peoples R China

Functions of bounded deformation (BD) are widely used in the theory of elastoplasticity to describe the possibly discontinuous displacement fields inside elastoplastic bodies. BD functions have been proved suitable for deformable image registration, the goal of which is to find the displacement field between a moving image and a fixed image. Recently BD functions have been generalized to symmetric tensor fields of bounded generalized variation. In this paper, we focus on the first-order symmetric tensor fields, i.e., vector-valued functions, of bounded generalized variation. We specify these functions as functions of bounded generalized deformation (BGD) since BGD functions are natural generalizations of BD functions. We propose a BGD model for deformable image registration problems by regarding concerned displacement fields as BGD functions. BGD model employs not only the first-order but also higher-order coupling information of components of the displacement field. It turns out that BGD model allows for jump discontinuities of displacements while, in contrast to BD model, at the same time is able to employ higher-order derivatives of displacements in smooth regions. As a result, BGD model tends to capture possible discontinuities of displacements appeared around edges of the target objects while keep the smoothness of displacements inside the target objects as well. This characteristic enables BGD model to obtain better registration results than BD model and other variational models. To our knowledge, it is the first time in literature to use BGD functions for image registration. A first-order adaptive primal-dual algorithm is adopted to solve the proposed BGD model. Numerical experiments on 2D and 3D images show both effectiveness and advantages of BGD model.

关键词： Functions of bounded generalized deformation Deformable image registration Functions of bounded deformation Primal– dual algorithm

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A high order PDE-constrained optimization for the image denoising problem

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INVERSE PROBLEMS IN SCIENCE AND ENGINEERING 2021年第12期29卷 1821-1863页

作者： Afraites, Lekbir Hadri, Aissam Laghrib, Amine Nachaoui, Mourad Univ Sultan Moulay Slimane LMA FST Beni Mellal Beni Mellal Morocco Univ Ibn Zohr Fac Polydisciplinaire Ouarzazate Morocco

In the present work, we investigate the inverse problem of identifying simultaneously the denoised image and the weighting parameter that controls the balance between two diffusion operators for an evolutionary partial differential equation (PDE). The problem is formulated as a non-smooth PDE-constrained optimization model. This PDE is constructed by second- and fourth-order diffusive tensors that combines the benefits from the diffusion model of Perona-Malik in the homogeneous regions, the Weickert model near sharp edges and the fourth-order term in reducing staircasing. The existence and uniqueness of solutions for the proposed PDE-constrained optimization system are provided in a suitable Sobolev space. Also, an optimization problem for the determination of the weighting parameter is introduced based on the Primal-dual algorithm. Finally, simulation results show that the obtained parameter usually coincides with the better choice related to the best restoration quality of the image.

关键词： Image restoration PDE-constrained parameter identification primal– dual algorithm tensor diffusion

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