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A decomposition method for solving multicommodity network equilibria

OPERATIONS RESEARCH LETTERS 2022年第1期50卷 40-44页

作者： Bui, Minh N. North Carolina State Univ Dept Math Raleigh NC 27695 USA

We consider the numerical aspect of the multicommodity network equilibrium problem proposed by Rockafellar in 1995. Our method relies on the flexible monotone operator splitting framework recently proposed by Combette... 详细信息

关键词： Network equilibrium Network flow Traffic assignment splitting algorithm Block-iterative algorithm Monotone operator

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splitting augmented Lagrangian-type algorithms with partial quadratic approximation to solve sparse signal recovery problems

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2024年 449卷

作者： Jian, Jinbao Huang, Qiongxuan Yin, Jianghua Zhang, Wei Guangxi Minzu Univ Ctr Appl Math Guangxi Sch Math & Phys Nanning 530006 Peoples R China

In this paper, we focus on the two -block nonconvex and nonsmooth optimization with linear constraints, where the objective function is the sum of a convex but nonsmooth function and a smooth but nonconvex function. This problem encompasses many important applications in engineering and machine learning. Based on the splitting algorithm, making use of the quadratic approximation of the smooth part, and with the help of Armijo line search technique, we first propose a splitting augmented Lagrangian method with partial quadratic approximation. Under some mild conditions, the global convergence of the proposed method is proved. Moreover, when the gradient of the smooth part in the objective function is Lipschitz continuous, we then propose and analyze a variant of the aforementioned method without performing line search. We report some preliminary numerical results on solving nonconvex quadratic regularization problems to show the feasibility and effectiveness of the two proposed methods. Finally, we show applicability and encouraging efficiency of our methods by applying them to solve sparse signal recovery problems.

关键词： Augmented Lagrangian method splitting algorithm Second-order information Line search Global convergence

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Effective neighborhood search with optimal splitting and adaptive memory for the team orienteering problem with time windows

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COMPUTERS & OPERATIONS RESEARCH 2020年 123卷 105039-105039页

作者： Amarouche, Youcef Guibadj, Rym Nesrine Chaalal, Elhadja Moukrim, Aziz Agence Environm & Maitrise & Energie 20 Ave GresilleBP 90406 F-49004 Angers 01 France Univ Technol Compiegne Sorbonne Univ CNRS Heudiasyc UMR 7253 CS 60319 F-60203 Compiegne France Univ Littoral Cote dOpale EA 4491 LISIC Lab Informat Signal & Image Cote Opale F-62228 Calais France Orange Labs Networks F-22300 Lannion France

The Team Orienteering Problem with Time Windows (TOPTW) is an extension of the well-known Orienteering Problem. Given a set of locations, each one associated with a profit, a service time and a time window, the objective of the TOPTW is to plan a set of routes, over a subset of locations, that maximizes the total collected profit while satisfying travel time limitations and time window constraints. Within this paper, we present an effective neighborhood search for the TOPTW based on (1) the alternation between two different search spaces, a giant tour search space and a route search space, using a powerful splitting algorithm, and (2) the use of a long term memory mechanism to keep high quality routes encountered in elite solutions. We conduct extensive computational experiments to investigate the contribution of these components, and measure the performance of our method on literature benchmarks. Our approach outperforms state-of-the-art algorithms in terms of overall solution quality and computational time. It finds the current best known solutions, or better ones, for 89% of the literature instances within reasonable runtimes. Moreover, it is able to achieve better average deviation than state-of-the-art algorithms within shorter computation times. Moreover, new improvements for 57 benchmark instances were found. (C) 2020 Elsevier Ltd. All rights reserved.

关键词： Routing Team orienteering problem Time windows Adaptive memory splitting algorithm Heuristics

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Revocable Sliced CipherText Policy Attribute Based Encryption Scheme in Cloud Computing 15

Revocable Sliced CipherText Policy Attribute Based Encryptio...

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15th IEEE International Wireless Communications and Mobile Computing Conference (IEEE IWCMC)

作者： Bouchaala, Mariem Ghazel, Cherif Saidane, Leila Azouz Univ Manouba Tunisia ENSI CRISTAL Lab Manouba Tunisia

ISBN: (纸本)9781538677476

Cloud Computing is the most promising paradigm in recent times. It offers a cost-efficient service to individual and industries. However, outsourcing sensitive data to entrusted Cloud servers presents a brake to Cloud migration. Consequently, improving the security of data access is the most critical task. As an efficient cryptographic technique, Ciphertext Policy Attribute Based Encryption(CP-ABE) develops and implements fine-grained, flexible and scalable access control model. However, existing CP-ABE based approaches suffer from some limitations namely revocation, data owner overhead and computational cost. In this paper, we propose a sliced revocable solution resolving the aforementioned issues abbreviated RS-CPABE. We applied splitting algorithm. We execute symmetric encryption with Advanced Encryption Standard (AES)in large data size and asymmetric encryption with CP-ABE in constant key length. We re-encrypt in case of revocation one single slice. To prove the proposed model, we expose security and performance evaluation.

关键词： Cloud access control CipherText Policy Attribute Based Encryption revocation splitting algorithm Advanced Encryption Standard

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New Demiclosedness Principles for (Firmly) Nonexpansive Operators 1

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Workshop on Computational and Analytical Mathematics

作者： Bauschke, Heinz H. Univ British Columbia Dept Math Kelowna BC V1V 1V7 Canada

ISBN: (数字)9781461476214

ISBN: (纸本)9781461476214;9781461476207

The demiclosedness principle is one of the key tools in nonlinear analysis and fixed point theory. In this note, this principle is extended and made more flexible by two mutually orthogonal affine subspaces. Versions for finitely many (firmly) nonexpansive operators are presented. As an application, a simple proof of the weak convergence of the Douglas-Rachford splitting algorithm is provided.

关键词： Demiclosedness principle Douglas-Rachford algorithm Firmly nonexpansive mapping Maximal monotone operator Nonexpansive mapping Proximal algorithm Resolvent splitting algorithm

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A Multi Linear Regression Approach for Handling Missing Values with Unknown Dependent Variable (MLRMUD) 14

A Multi Linear Regression Approach for Handling Missing Valu...

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14th International Computer Engineering Conference (ICENCO)

作者： Karama, Ahmed Farouk, Mona Atiya, Amir Cairo Univ Comp Engn Cairo Egypt

ISBN: (纸本)9781538651179

many problems in data applications are plagued with missing values. The Missing Value problem (MV) is the problem of predicting these missing values, in an attempt to make full use of the data. Simply deleting the missing record will waste precious information. In this work a new approach is proposed, the so-called MLRMUD. It is based on Multiple Linear Regression is used to predict Missing values for a data set with Unknown Dependent variable. It is applicable if complete rows are at least 20%. If they are less than that the Mean method is used to fill some rows until the complete rows reach 20%. After that MLRMUD can be applied normally. This approach is composed of three algorithms;splitting algorithm, dependent variable selection algorithm and multi-linear regression algorithm. MLRMUD is compared to other methods in the literature where it is proved that it outperforms them all in the accuracy of missing value computation determined in terms of to Root Mean Square Error (RMSE) and Mean Standard Error (MSE). A method to determine the unknown, dependent variable from the training set is proposed. The results show that the proposed method can successfully select the dependent variable with an accuracy of 83% over all the datasets examined.

关键词： missing values splitting algorithm dependent variable multi linear regression regression coefficients

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A Perturbation Framework for Convex Minimization and Monotone Inclusion Problems with Nonlinear Compositions

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MATHEMATICS OF OPERATIONS RESEARCH 2024年第3期49卷 1890-1914页

作者： Briceno-Arias, Luis M. Combettes, Patrick L. Univ Tecn Federico Santa Maria Dept Matemat Santiago 8940897 Chile North Carolina State Univ Dept Math Raleigh NC 27695 USA

We introduce a framework based on Rockafellar's perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions. Such problems have been investigated only from a primal perspective and only for nonlinear compositions of smooth functions in finite-dimensional spaces in the absence of linear compositions. In the context of Banach spaces, the proposed perturbation analysis serves as a foundation for the construction of a dual problem and of a maximally monotone Kuhn-Tucker operator, which is decomposable as the sum of simpler monotone operators. In the Hilbertian setting, this decomposition leads to a block-iterative primal-dual algorithm that fully splits all the components of the problem and appears to be the first proximal splitting algorithm for handling nonlinear composite problems. Various applications are discussed.

关键词： convex optimization duality monotone operator nonlinear composition perturbation theory proximal method splitting algorithm

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Solving monotone inclusions involving the sum of three maximally monotone operators and a cocoercive operator with applications

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SET-VALUED AND VARIATIONAL ANALYSIS 2023年第2期31卷 16-16页

作者： Zong, Chunxiang Tang, Yuchao Zhang, Guofeng Lanzhou Univ Sch Math & Stat Lanzhou 730000 Peoples R China Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Peoples R China

In this paper, we propose two four-operator splitting algorithms for approaching the set of zeros of the sum of three maximally monotone operators and a cocoercive operator. Our methods do not rely on the traditional product space technique. The sequences of the proposed algorithms are proven to be convergent under mild conditions. In applications of interest to us, we employ the proposed algorithms to solve a composite convex minimization problem, for which we also provide convergence analysis. Numerical experiments are performed on the image inpainting problem to demonstrate the efficiency of the proposed algorithms.

关键词： Monotone inclusion splitting algorithm Cocoercive operator Image inpainting

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A BARYCENTRIC PROJECTED-SUBGRADIENT algorithm FOR EQUILIBRIUM PROBLEMS

JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS

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JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS 2017年第1期1卷 43-59页

作者： Dang Van Hieu Moudafi, Abdellatif Vietnam Natl Univ Dept Math 334 Nguyen Trai Hanoi Vietnam Aix Marseille Univ CNRS LIS UMR 7296 F-13397 Marseille France

This paper deals with an algorithm for approximating solutions of equilibrium problems in Hilbert spaces. We describe how to incorporate the diagonal subgradient and the projection methods, and then establish that the resulting algorithm is strongly convergent under mild conditions. To demonstrate the effectiveness and convergence of the algorithm, we provided numerical comparisons of the algorithm with four existing algorithms. The comparisons suggested that the algorithm is effective for solving equilibrium problems.

关键词： Diagonal subgradient method Equilibrium problem Monotone bifunction Pseudomonotone bifunction splitting algorithm

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Collision Resolution for TETRA Systems

ITG-Fachbericht

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ITG-Fachbericht 1998年第145期 559-565页

作者： Steppler, Martin Buter, Michael Aachen University of Technology Department for Communication Netwoks Prof. Dr.-Ing. Bernhard Walke Kopernikusstr. 16 D-52074 Aachen Germany

This paper gives an inside look into the TETRA PDO random access protocol. Several collision resolution schemes are adapted to PDO and then evaluated by means of simulation.

关键词： Collision resolution Data sense multiple access (DSMA) Exponential backoff Minimum mean-squared error Packet Data Optimised (PDO) Pseudo-Bayesian Random access Slotted ALOHA splitting algorithm Stochastic approximation TETRA

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