Opportunistic selection is a key technique to improve the performance of wireless systems. In it, one among the available users is selected on the basis of their channel gains or local parameters, such as battery ener...
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Opportunistic selection is a key technique to improve the performance of wireless systems. In it, one among the available users is selected on the basis of their channel gains or local parameters, such as battery energy state. Formally, each user possesses a real-valued metric that only it knows, and the goal is to select the best user, which has the highest metric. The splitting algorithm is a popular, fast, and scalable algorithm to implement opportunistic selection;it is distributed and guarantees selection of the best user. We show that this algorithm, which has thus far been designed assuming that the metrics are independent and identically distributed, is no longer scalable when the metrics are correlated. We then propose a novel correlation-aware splitting algorithm (CASA) and show how it can be applied to practically motivated probability distributions and correlation models. We present computationally feasible techniques for pre-computing the thresholds that CASA specifies, thereby ensuring that CASA can be implemented in practice. We benchmark the performance of CASA with the conventional algorithm, and show that it reduces the average selection time significantly as the number of users or the correlation among them increases.
This note is devoted to the splitting algorithm proposed by Davis and Yin (Set-valued Var. Anal. 25(4), 829-858, 2017) for computing a zero of the sum of three maximally monotone operators, with one of them being coco...
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This note is devoted to the splitting algorithm proposed by Davis and Yin (Set-valued Var. Anal. 25(4), 829-858, 2017) for computing a zero of the sum of three maximally monotone operators, with one of them being cocoercive. We provide a direct proof that guarantees its convergence when the stepsizes are smaller than four times the cocoercivity constant, thus doubling the size of the interval established by Davis and Yin. As a by-product, the same conclusion applies to the forward-backward splitting algorithm. Further, we use the notion of "strengthening" of a set-valued operator to derive a new splitting algorithm for computing the resolvent of the sum. Last but not least, we provide some numerical experiments illustrating the importance of appropriately choosing the stepsize and relaxation parameters of the algorithms.
In this paper, we focus on a numerical method of a problem called the Perona-Malik inequality which we use for image denoising. This model is obtained as the limit of the Perona-Malik model and the p-Laplacian operato...
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In this paper, we focus on a numerical method of a problem called the Perona-Malik inequality which we use for image denoising. This model is obtained as the limit of the Perona-Malik model and the p-Laplacian operator with p -> infinity. In Atlas et al., (Nonlinear Anal. Real World Appl 18:57-68, 2014), the authors have proved the existence and uniqueness of the solution of the proposed model. However, in their work, they used the explicit numerical scheme for approximated problem which is strongly dependent to the parameter p. To overcome this, we use in this work an efficient algorithm which is a combination of the classical additive operator splitting and a nonlinear relaxation algorithm. At last, we have presented the experimental results in image filtering show, which demonstrate the efficiency and effectiveness of our algorithm and finally, we have compared it with the previous scheme presented in Atlas et al., (Nonlinear Anal. Real World Appl 18:57-68, 2014).
In this article, we highlight a bias induce by the discretization of the sample Markov paths in the splitting algorithm. Consequently we propose to correct this bias using a deformation of the intermediate regions. Mo...
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In this article, we highlight a bias induce by the discretization of the sample Markov paths in the splitting algorithm. Consequently we propose to correct this bias using a deformation of the intermediate regions. Moreover, we propose two estimation methods of the optimal regions in the splitting algorithm to minimise the splitting variance. One is connected with partial differential equation approach, the other one is based on the discretization of the state space of the process. (C) 2015 Elsevier B.V. All rights reserved.
作者：
ZHU, CYEECS Department
2145 Sheridan Road Northwestern University Evanston Illinois 60208-3118
The asymptotic convergence of the forward-backward splitting algorithm for solving equations of type 0 is an element of T(z) is analyzed, where T is a multivalued maximal monotone operator in the n-dimensional Euclide...
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The asymptotic convergence of the forward-backward splitting algorithm for solving equations of type 0 is an element of T(z) is analyzed, where T is a multivalued maximal monotone operator in the n-dimensional Euclidean space, When the problem has a nonempty solution set, and T is split in the form T = J + h It with J being maximal monotone and h being co-coercive with modulus greater than 1/2, convergence rates are shown, under mild conditions, to be linear, superlinear or sublinear depending on how rapidly J(-1) and h(-1) grow in the neighborhoods of certain specific points. As a special case, when both J and h are polyhedral functions, we get R-linear convergence and 2-step e-linear convergence without any further assumptions on the strict monotonicity on T or on the uniqueness of the solution. As another special case when h = 0, the splitting algorithm reduces to the proximal point algorithm, and we get new results, which complement R. T. Rockafellar's and F. J. Luque's earlier results on the proximal point algorithm.
In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed wi...
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In this work, we study resolvent splitting algorithms for solving composite monotone inclusion problems. The objective of these general problems is finding a zero in the sum of maximally monotone operators composed with linear operators. Our main contribution is establishing the first primal-dual splitting algorithm for composite monotone inclusions with minimal lifting. Specifically, the proposed scheme reduces the dimension of the product space where the underlying fixed point operator is defined, in comparison to other algorithms, without requiring additional evaluations of the resolvent operators. We prove the convergence of this new algorithm and analyze its performance in a problem arising in image deblurring and denoising. This work also contributes to the theory of resolvent splitting algorithms by extending the minimal lifting theorem recently proved by Malitsky and Tam to schemes with resolvent parameters.
In this paper, we present a viscosity splitting algorithm with computational errors for solving common solutions of inclusion and equilibrium problems. Strong convergence theorems are established in the framework of r...
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In this paper, we present a viscosity splitting algorithm with computational errors for solving common solutions of inclusion and equilibrium problems. Strong convergence theorems are established in the framework of real Hilbert spaces. Applications are also provided to support the main results.
We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We...
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We consider the problem of finding a fixed point of a nonexpansive mapping, which is also a solution of a pseudo-monotone equilibrium problem, where the bifunction in the equilibrium problem is the sum of two ones. We propose a splitting algorithm combining the gradient method for equilibrium problem and the Mann iteration scheme for fixed points of nonexpansive mappings. At each iteration of the algorithm, two strongly convex subprograms are required to solve separately, one for each of the component bifunctions. Our main result states that, under paramonotonicity property of the given bifunction, the algorithm converges to a solution without any Lipschitz-type condition as well as Holder continuity of the bifunctions involved.
作者：
Khammahawong, K.Kumam, P.Chaipunya, P.KMUTT
Dept Math 126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT
KMUTTFixed Point Res Lab KMUTTFixed Point Theory & Applicat Res Grp Dept MathFac Sci 126 Pracha Uthit Rd Bangkok 10140 Thailand KMUTT
Ctr Excellence Theoret & Computat Sci TaCS CoE SCL 802 Fixed Point Lab Sci Lab Bldg126 Pracha Uthit Rd Bangkok 10140 Thailand
The aim of this paper is to introduce a splitting algorithm to solving mixed equilibrium problems on a Hadamard manifold. The convergence of the sequence generated by the proposed algorithm is established under suitab...
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The aim of this paper is to introduce a splitting algorithm to solving mixed equilibrium problems on a Hadamard manifold. The convergence of the sequence generated by the proposed algorithm is established under suitable assumptions.
We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the al...
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We propose a primal-dual splitting algorithm for solving monotone inclusions involving a mixture of sums, linear compositions, and parallel sums of set-valued and Lipschitzian operators. An important feature of the algorithm is that the Lipschitzian operators present in the formulation can be processed individually via explicit steps, while the set-valued operators are processed individually via their resolvents. In addition, the algorithm is highly parallel in that most of its steps can be executed simultaneously. This work brings together and notably extends various types of structured monotone inclusion problems and their solution methods. The application to convex minimization problems is given special attention.
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