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On the Search algorithm for the Output Distribution That Achieves the Channel Capacity

IEEE TRANSACTIONS ON INFORMATION THEORY 2017年第2期63卷 1043-1062页

作者： Nakagawa, Kenji Watabe, Kohei Sabu, Takuto Nagaoka Univ Technol Dept Elect & Elect & Informat Engn Nagaoka Niigata 9402188 Japan

We consider a search algorithm for the output distribution that achieves the channel capacity of a discrete memoryless channel. We will propose an algorithm by iterated projections of an output distribution onto affine subspaces in the set of output distributions. The problem of channel capacity has a similar geometric structure as that of smallest enclosing circle for a finite number of points in the Euclidean space. The metric in the Euclidean space is the Euclidean distance and the metric in the space of output distributions is the Kullback-Leibler divergence. We consider these two problems based on Amari's a-geometry. Then, we first consider the smallest enclosing circle in the Euclidean space and develop an algorithm to find the center of the smallest enclosing circle. Based on the investigation, we will apply the obtained algorithm to the problem of channel capacity.

关键词： Channel capacity discrete memoryless channel smallest enclosing circle information geometry projection algorithm

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Experimental and numerical investigation of nanofluid heat transfer in helically coiled tubes at constant wall temperature using dispersion model

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2013年第1-2期58卷 480-491页

作者： Akbaridoust, Farzan Rakhsha, Milad Abbassi, Abbas Saffar-Awal, Majid Amirkabir Univ Technol Tehran Polytech Dept Mech Engn Tehran Iran

In the present research, laminar, steady state flow in helically coiled tubes at a constant wall temperature was studied numerically and experimentally. Pressure drop and the convective heat transfer behavior of nanofluid were investigated. In the experimental section, a heat exchanger was designed, capable of providing constant wall temperature for coils with different curvature and torsion ratio for the ease of assembly. Pressure drop measurement and average convective heat transfer coefficient calculation were carried out. In the numerical study, the three dimensional governing equations were solved by finite difference method with projection algorithm using FORTRAN programming language. Homogeneous model with constant effective properties was used. The difference between numerical and experimental results was significant. Dispersion model was employed to make the observed difference between numerical and experimental results negligible. Dispersion model was modified to be applicable for helical tubes. This modification resulted in negligible difference between the numerical and the experimental results. More enhanced heat transfer was observed for tubes with greater curvature ratio. Moreover, the performance evaluation of these enhanced heat transfer methods presented. Utilization of base fluid in helical tube with greater curvature compared to the use of nanofluid in straight tubes enhanced heat transfer more effectively. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Nanofluid Helically coiled tube projection algorithm Homogeneous dispersion model Constant wall temperature Experimental setup

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Distributed Containment Control of Fractional-order Multi-agent Systems with Double-integrator and Nonconvex Control Input Constraints

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INTERNATIONAL JOURNAL OF CONTROL AUTOMATION AND SYSTEMS 2020年第7期18卷 1728-1742页

作者： Yuan, Xiao-Lin Mo, Li-Po Yu, Yong-Guang Ren, Guo-Jian Beijing Technol & Business Univ Sch Math & Stat 11 FuCheng Rd Beijing 100048 Peoples R China Beijing Jiaotong Univ Dept Math 3 ShangYuanCun Beijing 100044 Peoples R China

This paper mainly considers the distributed containment control problem for continuous-time fractional-order multi-agent systems (FOMASs) with double-integrator, where the control input of each agent is constrained to lie in a nonconvex set. A distributed projection containment control algorithm is designed for each follower. To finish the convergence analysis, the original closed-loop system is first changed into an equivalent one by a proper model transformation and the method of the L-1 interpolation approximation is introduced to deal with the projection operator. Then, by using the properties of the convex hull and the Mittag-Leffler function, it is shown that the largest distance between the followers and the convex hull spanned by leaders tends to zero asymptotically, while all agents' control inputs are constrained to stay in their corresponding nonconvex constraint sets. Finally, numerical simulations are provided to verify the effectiveness of the theoretical results.

关键词： Distributed containment control fractional-order multi-agent systems nonconvex constrains projection algorithm

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A Novel Method for Solving Nonmonotone Equilibrium Problems

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MEDITERRANEAN JOURNAL OF MATHEMATICS 2024年第7期21卷 1-28页

作者： Thanh, Tran Thi Huyen Manh, Hy Duc Ha, Nguyen Thi Thanh Dinh, Bui Van Le Quy Don Tech Univ Fac Informat Technol Dept Math Hanoi Vietnam

In this paper, we propose a novel projection method for finding a solution of equilibrium problems EP(C, f) in Euclidean spaces in which the bifunction does not require to be satisfied any monotonicity. Unlike methods for solving such a problem used in the literature, shrinking projection methods which may raise cost of computation, we suggest using an adaptive projection method incorporate with linesearch procedures to solve these problems when the bifunction does not satisfy the Lipschitz-type condition. These linesearches are unnecessary when f satisfies the Lipschitz-type condition with constants L1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_1$$\end{document} and L2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$L_2$$\end{document}. In case these constants are unknown, we propose to use the adaptive step sizes. All algorithms are proven to converge to a solution of the considered problem, and some numerical examples are also reported to illustrate the efficiency of the proposed algorithms.

关键词： Nonmonotonicity Equilibrium problem projection algorithm Armijo linesearch Lipschitz-type condition

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A modified Solodov-Svaiter method for solving nonmonotone variational inequality problems

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NUMERICAL algorithmS 2022年第4期90卷 1715-1734页

作者： Bui Van Dinh Hy Duc Manh Tran Thi Huyen Thanh Le Quy Don Tech Univ Fac Informat Technol Dept Math Hanoi Vietnam VAST Inst Math Dept Optimizat & Control Theory Hanoi Vietnam

In a very interesting paper (SIAM J. Control Optim. 37(3): 765-776, 1999), Solodov and Svaiter introduced an effective projection algorithm with linesearch for finding a solution of a variational inequality problem (VIP) in Euclidean space. They showed that the iterative sequence generated by their algorithm converges to a solution of (VIP) under the main assumption that the cost mapping is pseudomonotone and continuous. In this paper, we propose to modify this algorithm for solving variational inequality problems in which the cost mapping is not required to be satisfied any pseudomonotonicity. Moreover, we do not use the embedded projection methods as in methods used in literature and the linesearch procedure is not necessary when the cost mapping is Lipschitz. Several numerical examples are also provided to illustrate the efficient of the proposed algorithms.

关键词： Non-monotonicity Variational inequalities projection algorithm Armijo linesearch

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DYNAMIC PROGRAMMING TECHNIQUE IN MULTI UAVS FORMATION ANOMALY DETECTION

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INTERNATIONAL JOURNAL OF INNOVATIVE COMPUTING INFORMATION AND CONTROL 2018年第6期14卷 1977-1991页

作者： Wang, Jianhong Wang, Yanxiang Jiangxi Univ Sci & Technol Sch Elect Engn & Automat 86 Hongqi Ave Ganzhou 341000 Peoples R China

To deal with the problem of anomaly detection in multi UAVs formation, and simplify the complexity of hypothesis testing or probability inequalities, the anomaly detection problem can be transformed to identify some unknown parameters process. To avoid a statistical description on measurement noise, a worthwhile alternative is the bounded noise characterization. In the presence of bounded noise, the projection algorithm with dead zone and its modified form are proposed to identify the unknown parameters, such that the robustness of projection algorithm can be enhanced by increasing a dead zone. Furthermore, dynamic programming technique is introduced to balance the desire for lower present cost with the undesirability of high future cost in determining the anomaly detector, and then the cost of collecting new observations and the higher probability of accepting the wrong hypothesis can be compensated. A numerical example illustrates the characteristic of the anomaly detection problem.

关键词： Multi UAVs formation Anomaly detection projection algorithm Dynamic programming Dead zone

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Nonconvex Differential Variational Inequality and State-Dependent Sweeping Process

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2013年第2期159卷 386-398页

作者： Haddad, Tahar Univ Jijel Fac Sci & Informat Lab Math Pures & Appl Jijel 18000 Algeria

We prove the existence of solutions of a differential variational inequality involving a prox-regular set in an infinite dimensional Hilbert space via a new existence result of a non-convex state-dependent sweeping pr... 详细信息

关键词： Differential variational inequality projection algorithm Prox-regular sets Normal cones

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Solution of Navier-Stokes equations in primitive variables by diffuse approximation

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE II FASCICULE...

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COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE II FASCICULE B-MECANIQUE PHYSIQUE ASTRONOMIE 1998年第2期326卷 117-119页

作者： Couturier, S Sadat, H Ecole Natl Super Mecan & Aerotech UMR 6068 Lab Etud Therm F-86960 Chasseneuil Futuroscope France

A diffuse approximation method for solving Navier-Stokes equations in primitive variables is proposed. The results of a numerical example show the accuracy and efficiency of this approach. (C) Academie des Sciences/El... 详细信息

关键词： diffuse approximation driven cavity projection algorithm

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Global convergence of a non-convex Douglas-Rachford iteration

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JOURNAL OF GLOBAL OPTIMIZATION 2013年第3期57卷 753-769页

作者： Artacho, Francisco J. Aragon Borwein, Jonathan M. Univ Newcastle Ctr Comp Assisted Res Math & Its Applicat CARMA Callaghan NSW 2308 Australia King Abdulaziz Univ Jeddah 21413 Saudi Arabia

We establish a region of convergence for the proto-typical non-convex Douglas-Rachford iteration which finds a point on the intersection of a line and a circle. Previous work on the non-convex iteration Borwein and Sims (Fixed-point algorithms for inverse problems in science and engineering, pp. 93-109, 2011) was only able to establish local convergence, and was ineffective in that no explicit region of convergence could be given.

关键词： Non-convex feasibility problem Fixed point theory projection algorithm Douglas-Rachford algorithm Global convergence Signal reconstruction

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projection methods for high numerical aperture phase retrieval

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INVERSE PROBLEMS 2021年第12期37卷 125005-125005页

作者： Nguyen Hieu Thao Soloviev, Oleg Luke, Russell Verhaegen, Michel Delft Univ Technol Delft Ctr Syst & Control NL-2628 CD Delft Netherlands Can Tho Univ Sch Educ Dept Math Can Tho Vietnam Flexible Opt BV Polakweg 10-11 NL-2288 GG Rijswijk Netherlands Univ Gottingen Inst Numer & Angew Math D-37083 Gottingen Germany

We develop for the first time a mathematical framework in which the class of projection algorithms can be applied to high numerical aperture (NA) phase retrieval. Within this framework, we first analyze the basic steps of solving the high-NA phase retrieval problem by projection algorithms and establish the closed forms of all the relevant projection operators. We then study the geometry of the high-NA phase retrieval problem and the obtained results are subsequently used to establish convergence criteria of projection algorithms in the presence of noise. Making use of the vectorial point-spread-function (PSF) is, on the one hand, the key difference between this paper and the literature of phase retrieval mathematics which deals with the scalar PSF. The results of this paper, on the other hand, can be viewed as extensions of those concerning projection methods for low-NA phase retrieval. Importantly, the improved performance of projection methods over the other classes of phase retrieval algorithms in the low-NA setting now also becomes applicable to the high-NA case. This is demonstrated by the accompanying numerical results which show that available solution approaches for high-NA phase retrieval are outperformed by projection methods.

关键词： phase retrieval high numerical aperture projection algorithm nonconvex optimization inconsistent feasibility

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