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Dual Power Multiple Access with Multipacket Reception using Local CSI

IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS 2009年第8期8卷 4078-4088页

作者： Yim, Raymond Mehta, Neelesh B. Molisch, Andreas F. Zhang, Jinyun MERL Cambridge MA USA Indian Inst Sci Elect Commun Eng Dept Bangalore 560012 Karnataka India Univ So Calif Los Angeles CA USA

Contention-based multiple access is a crucial component of many wireless systems. Multiple-packet reception (MPR) schemes that use interference cancellation techniques to receive and decode multiple packets that arrive simultaneously are known to be very efficient. However, the MPR schemes proposed in the literature require complex receivers capable of performing advanced signal processing over significant amounts of soft undecodable information received over multiple contention steps. In this paper, we show that local channel knowledge and elementary received signal strength measurements, which are available to many receivers today, can actively facilitate multi-packet reception and even simplify the interference canceling receiver's design. We introduce two variants of a simple algorithm called Dual Power Multiple Access (DPMA) that use local channel knowledge to limit the receive power levels to two values that facilitate successive interference cancellation. The resulting receiver structure is markedly simpler, as it needs to process only the immediate received signal without having to store and process signals received previously. Remarkably, using a set of three feedback messages, the first variant, DPMA-Lite, achieves a stable throughput of 0.6865 packets per slot. Using four possible feedback messages, the second variant, Turbo-DPMA, achieves a stable throughput of 0.793 packets per slot, which is better than all contention algorithms known to date.

关键词： splitting algorithms multiple access contention multiple packet reception collision power control successive interference cancelation receive signal strength indicator

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Customized proximal point algorithms for linearly constrained convex minimization and saddle-point problems: a unified approach

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2014年第1-2期59卷 135-161页

作者： Gu, Guoyong He, Bingsheng Yuan, Xiaoming Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China Nanjing Univ Int Ctr Management Sci & Engn Nanjing 210093 Jiangsu Peoples R China Nanjing Univ Dept Math Nanjing 210093 Jiangsu Peoples R China Hong Kong Baptist Univ Dept Math Hong Kong Hong Kong Peoples R China

This paper focuses on some customized applications of the proximal point algorithm (PPA) to two classes of problems: the convex minimization problem with linear constraints and a generic or separable objective function, and a saddle-point problem. We treat these two classes of problems uniformly by a mixed variational inequality, and show how the application of PPA with customized metric proximal parameters can yield favorable algorithms which are able to make use of the models' structures effectively. Our customized PPA revisit turns out to unify some algorithms including some existing ones in the literature and some new ones to be proposed. From the PPA perspective, we establish the global convergence and a worst-case O(1/t) convergence rate for this series of algorithms in a unified way.

关键词： Convex minimization Saddle-point problem Proximal point algorithm Convergence rate Customized algorithms splitting algorithms

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Forward-reflected-backward and shadow-Douglas-Rachford with partial inverse for solving monotone inclusions

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MATHEMATICAL METHODS OF OPERATIONS RESEARCH 2024年第3期100卷 723-752页

作者： Roldan, Fernando Univ Concepcion Dept Ingn Matemat Avda Esteban Iturra s-n Concepcion Chile

In this article, we study two methods for solving monotone inclusions in real Hilbert spaces involving the sum of a maximally monotone operator, a monotone-Lipschitzian operator, a cocoercive operator, and a normal cone to a vector subspace. Our algorithms split and exploits the intrinsic properties of each operator involved in the inclusion. We derive our methods by combining partial inverse techniques with the forward-half-reflected-backward algorithm and with the forward-shadow-Douglas-Rachford (FSDR) algorithm, respectively. Our methods inherit the advantages of those methods, requiring only one activation of the Lipschitzian operator, one activation of the cocoercive operator, two projections onto the closed vector subspace, and one calculation of the resolvent of the maximally monotone operator. Additionally, to allow larger step-sizes in one of the proposed methods, we revisit FSDR by extending its convergence for larger step-sizes. Furthermore, we provide methods for solving monotone inclusions involving a sum of maximally monotone operatores and for solving a system of primal-dual inclusions involving a mixture of sums, linear compositions, parallel sums, Lipschitzian operators, cocoercive operators, and normal cones. We apply our methods to constrained composite convex optimization problems as a specific example. Finally, in order to compare our methods with existing methods in the literature, we provide numerical experiments on constrained total variation least-squares optimization problems and computed tomography inverse problems. We obtain promising numerical results.

关键词： splitting algorithms Monotone operator theory Partial inverse Convex optimization Forward-reflected-backward Shadow-Douglas-Rachford

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Analysis of d-ARY tree algorithms with successive interference cancellation

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JOURNAL OF APPLIED PROBABILITY 2024年第3期61卷 1075-1105页

作者： Vogel, Quirin Deshpande, Yash Stefanovic, Cedomir Kellerer, Wolfgang Tech Univ Munich Sch Computat Informat & Technol Dept Math Munich Germany Tech Univ Munich Lehrstuhl Kommunikationsnnetze Sch Computat Informat & Technol Munich Germany Aalborg Univ Dept Elect Syst DK-2450 Kobenhavn SV Denmark

We calculate the mean throughput, number of collisions, successes, and idle slots for random tree algorithms with successive interference cancellation. Except for the case of the throughput for the binary tree, all the results are new. We furthermore disprove the claim that only the binary tree maximizes throughput. Our method works with many observables and can be used as a blueprint for further analysis.

关键词： Random access asymptotic analysis functional equation splitting algorithms

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On the asymptotic behavior of some algorithms

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RANDOM STRUCTURES & algorithms 2005年第2期27卷 235-250页

作者： Robert, P INRIA F-78153 Le Chesnay France

A simple approach is presented to study the asymptotic behavior of some algorithms with an underlying tree structure. It is shown that some asymptotic oscillating behaviors can be precisely analyzed without resorting to complex analysis techniques as it is usually done in this context. A new explicit representation of periodic functions involved is obtained at the same time. (c) 2005 Wiley Periodicals, Inc.

关键词： splitting algorithms asymptotic oscillating behavior Poisson transform Mellin transform Ethernet tree communication protocol

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A mobile sensor network tracking moving targets in a dynamic environment

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IFAC-PapersOnLine 2015年第5期28卷 1-6页

作者： Dang, Anh Duc Horn, Joachim Institute of Control Engineering Helmut-Schmidt-University University of the Federal Armed Forces Hamburg Holstenhofweg 85 HamburgD-22043 Germany

This paper presents a novel approach to control a mobile sensor network to track moving targets in a dynamic environment. In this approach, we solve two main issues: the sensor splitting and merging control when the number of the targets is changed. The subgroup merging into the main group is controlled by the invariable attractive force field of the virtual leader in the main swarm. In other words, under the effect of this attractive force field, free-sensors can easily reach the main group and become new members in formation of this group. In contrast, subgroups will be split from the existing group to track new targets that appear. The splitting algorithm is built based on the geometry between targets and group position. The members in a split subgroup will connect with their neighbors in order to generate a robust formation without collision while tracking their target. In addition, when a target disappears, the sensors that are tracking this target will automatically distribute into the nearest existing subgroup. The effectiveness of this proposed approach has been verified in simulations. © 2015, IFAC. Hosting by Elsevier Ltd.

关键词： Target tracking Collision avoidance Merging Sensor networks Swarm intelligence Attractive force Dynamic environments Formation control Mobile sensor networks splitting algorithms splitting and merging Tracking moving targets Vector fields

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A Projected Primal-Dual Method for Solving Constrained Monotone Inclusions

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2019年第3期180卷 907-924页

作者： Briceno-Arias, Luis Lopez Rivera, Sergio Univ Tecn Federico Santa Maria Dept Matemat Santiago Chile

In this paper, we provide an algorithm for solving constrained composite primal-dual monotone inclusions, i.e., monotone inclusions in which a priori information on primal-dual solutions is represented via closed and convex sets. The proposed algorithm incorporates a projection step onto the a priori information sets and generalizes methods proposed in the literature for solving monotone inclusions. Moreover, under the presence of strong monotonicity, we derive an accelerated scheme inspired on the primal-dual algorithm applied to the more general context of constrained monotone inclusions. In the particular case of convex optimization, our algorithm generalizes several primal-dual optimization methods by allowing a priori information on solutions. In addition, we provide an accelerated scheme under strong convexity. An application of our approach with a priori information is constrained convex optimization problems, in which available primal-dual methods impose constraints via Lagrange multiplier updates, usually leading to slow algorithms with unfeasible primal iterates. The proposed modification forces primal iterates to satisfy a selection of constraints onto which we can project, obtaining a faster method as numerical examples exhibit. The obtained results extend and improve several results in the literature.

关键词： Accelerated schemes Constrained convex optimization Monotone operator theory Proximity operator splitting algorithms

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A probabilistic analysis of some tree algorithms

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ANNALS OF APPLIED PROBABILITY 2005年第4期15卷 2445-2471页

作者： Mohamed, H Robert, P INRIA F-78153 Le Chesnay France

In this paper a general class of tree algorithms is analyzed. It is shown that, by using an appropriate probabilistic representation of the quantities of interest, the asymptotic behavior of these algorithms can be obtained quite easily without resorting to the usual complex analysis techniques. This approach gives a unified probabilistic treatment of these questions. It simplifies and extends some of the results known in this domain.

关键词： splitting algorithms divide and conquer algorithms unusual laws of large numbers asymptotic oscillating behavior data structures tries renewal theorem

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APPLICATION OF ACCRETIVE-OPERATORS THEORY TO THE RADIATIVE-TRANSFER EQUATIONS: 收藏
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引用; SIAM JOURNAL ON MATHEMATICAL ANALYSIS 1987年第2期18卷 393-408页; 作者： MERCIER, B; Under some restrictive assumptions about opacities, we show that the radiative transfer equations have the form (d<span class="mi" id="MathJax-Span-9" style="font-family:; Under some restrictive assumptions about opacities, we show that the radiative transfer equations have the form $(d u / d t) + A u + B u = 0$; 来源：评论; 学校读者我要写书评

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An Introduction to Convexity, Optimization, and algorithms

An Introduction to Convexity, Optimization, and Algorithms

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丛书名： MOS-SIAM Series on Optimization

2023年

作者： Heinz H. Bauschke Walaa M. Moursi

ISBN: (数字)9781611977806

ISBN: (纸本)9781611977790

This concise, self-contained volume introduces convex analysis and optimization algorithms, with an emphasis on bridging the two areas. It explores cutting-edge algorithms-such as the proximal gradient, Douglas-Rachford, Peaceman-Rachford, and FISTA-that have applications in machine learning, signal processing, image reconstruction, and other fields.

An Introduction to Convexity, Optimization, and algorithms contains

algorithms illustrated by Julia examples,
more than 200 exercises that enhance the reader's understanding of the topic, and
clear explanations and step-by-step algorithmic descriptions that facilitate self-study for individuals looking to enhance their expertise in convex analysis and optimization.

关键词： convex analysis convex functions convex sets convex optimization Douglas-Rachford algorithm fast iterative soft thresholding algorithm Hilbert space Peaceman-Rachford algorithm projection mappings splitting algorithms proximal gradient method

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