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 affin...
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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.
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 nanof...
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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.
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...
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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.
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...
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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.
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 (V...
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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.
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 u...
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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.
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...
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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 process.
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...
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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/Elsevier, Paris.
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 Si...
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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.
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 step...
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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.
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