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An alternating algorithm for Finding Linear Arrow-Debreu Market Equilibria

THEORY OF COMPUTING SYSTEMS 2022年第1期66卷 38-55页

作者： Chen, Po-An Lu, Chi-Jen Lu, Yu-Sin Natl Yang Ming Chiao Tung Univ Inst Informat Management 1001 Univ Rd300 Hsinchu Taiwan Acad Sinica Inst Informat Sci 128 Acad RdSect 2 Taipei 11529 Taiwan Ind Technol Res Inst 195Sect 4Chung Hsing Rd Chutung Hsinchu County Taiwan

Motivated by the convergence result of mirror-descent algorithms to market equilibria in linear Fisher markets, it is natural for one to consider designing dynamics (specifically, iterative algorithms) for agents to arrive at linear Arrow-Debreu market equilibria. Jain (SIAM J. Comput. 37(1), 303-318,2007) reduced equilibrium computation in linear Arrow-Debreu markets to the equilibrium computation in bijective markets, where everyone is a seller of only one good and a buyer for a bundle of goods. In this paper, we design an algorithm for computing linear bijective market equilibrium, based on solving the rational convex program formulated by Devanur et al. The algorithm repeatedly alternates between a step of gradient-descent-like updates and a distributed step of optimization exploiting the property of such convex program. Convergence can be ensured by a new analysis different from the analysis for linear Fisher market equilibria.

关键词： Arrow-Debreu market equilibria Convex program alternating algorithm

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The alternating algorithm in a uniformly convex and uniformly smooth Banach space

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JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 2015年第1期421卷 747-753页

作者： Pinkus, Allan Technion Israel Inst Technol Dept Math IL-32000 Haifa Israel

Let X be a uniformly convex and uniformly smooth Banach space. Assume that the M-i, i = 1,..., r, are closed linear subspaces of X, P-Mi is the best approximation operator to the linear subspace M-i and M := M-1 +...+ M-r. We prove that if M is closed, then the alternating algorithm given by repeated iterations of (I - P-Mr) (I - PMr-1) ... (I - P-M1) applied to any x is an element of X converges to x - P(M)x is the best approximation Operator to the linear subspace M. This result, in the case r = 2, was proven in Deutsch [4]. (C) 2014 Elsevier Inc. All rights reserved.

关键词： alternating algorithm Uniformly convex Uniformly smooth

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A relaxed alternating CQ-algorithm for convex feasibility problems

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2013年第1期79卷 117-121页

作者： Moudafi, Abdellatif Univ Antilles Guyane Ceregmia Dept Sci Interfac F-97200 Schelcher Martinique France

Let H-1, H-2 H-3 be real Hilbert spaces, let C subset of H-1, Q subset of H-2 be two nonempty closed convex level sets, let A : H-1 -> H-3, B : H-2 -> H-3 be two bounded linear operators. Our interest is in solving the following new convex feasibility problem Find x is an element of C, y is an element of Q such that Ax = By, (1.1) which allows asymmetric and partial relations between the variables x and y. In this paper, we present and study the convergence of a relaxed alternating CQ-algorithm (RACQA) and show that the sequences generated by such an algorithm weakly converge to a solution of (1.1). The interest of RACQA is that we just need projections onto half-spaces, thus making the relaxed CQ-algorithm implementable. Note that, by taking B = I, in (1.1), we recover the split convex feasibility problem originally introduced in Censor and Elfving (1994) [13] and used later in intensity-modulated radiation therapy (Censor et al. (2006) [11]). We also recover the relaxed CQ-algorithm introduced by Yang (2004) [8] by particularizing both B and a given parameter. (C) 2012 Elsevier Ltd. All rights reserved.

关键词： Feasibility problem CQ-algorithm alternating algorithm

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The alternating simultaneous Halpern-Lions-Wittmann-Bauschke algorithm for finding the best approximation pair for two disjoint intersections of convex sets

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JOURNAL OF APPROXIMATION THEORY 2024年 301卷 106045页

作者： Censor, Yair Mansour, Rafiq Reem, Daniel Univ Haifa Dept Math IL-3498838 Haifa Israel Mawares E Thahab 2 POB 562 IL-44915 Tira Israel Univ Haifa Ctr Math & Sci Computat CMSC IL-3498838 Haifa Israel

Given two nonempty and disjoint intersections of closed and convex subsets, we look for a best approximation pair relative to them, i.e., a pair of points, one in each intersection, attaining the minimum distance between the disjoint intersections. We propose an iterative process based on projections onto the subsets which generate the intersections. The process is inspired by the Halpern-Lions-Wittmann- Bauschke algorithm and the classical alternating process of Cheney and Goldstein, and its advantage is that there is no need to project onto the intersections themselves, a task which can be rather demanding. We prove that under certain conditions the two interlaced subsequences converge to a best approximation pair. These conditions hold, in particular, when the space is Euclidean and the subsets which generate the intersections are compact and strictly convex. Our result extends the one of Aharoni, Censor and Jiang ["Finding a best approximation pair of points for two polyhedra", Computational Optimization and Applications 71 (2018), 509-23] who considered the case of finite-dimensional polyhedra.

关键词： alternating algorithm Best approximation pair Dini's Theorem Disjoint intersections Projection methods Simultaneous Halpern-Lions-Wittmann-Bauschke (S-HLWB) algorithm

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The Problem of Split Convex Feasibility and Its alternating Approximation algorithms

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Acta Mathematica Sinica,English Series 2015年第12期31卷 1857-1871页

作者： Zhen Hua HE Ji Tao SUN Department of Mathematics Tongji University Department of Mathematics Honghe University

This paper studies the problem of split convex feasibility and a strong convergent alternating algorithm is *** to this algorithm,some strong convergent theorems are obtained and an affirmative answer to the question ... 详细信息

关键词： alternating algorithm problem of split convex feasibility strong convergent theorem

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alternating Optimization for MIMO Secrecy Channel with a Cooperative Jammer 81

Alternating Optimization for MIMO Secrecy Channel with a Coo...

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81st IEEE Vehicular Technology Conference (VTC Spring)

作者： Chu, Zheng Johnston, Martin Le Goff, Stephane Newcastle Univ Sch Elect & Elect Engn Newcastle Upon Tyne NE1 7RU Tyne & Wear England

ISBN: (纸本)9781479980888

This paper proposes an alternating optimization algorithm for addressing the secrecy rate optimization problem for a multi-input-multi-output (MIMO) secrecy channel in the presence of a multiantenna eavesdropper, where a multiantenna cooperative jammer will be employed to confuse the eavesdropper by introducing jamming signal. We investigate the secrecy rate maximization problem, which is a non-convex problem in terms of transmit covariance matrices of the legitimate transmitter and the cooperative jammer. In order to circumvent this issue, we develop an optimization algorithm by alternating optimizing the transmit covariance matrices of the legitimate transmitter and the cooperative jammer where each transmit covariance matrix is optimized while other is fixed. Based on this algorithm, we develop a robust scheme by incorporating channel uncertainties associated with the eavesdropper. By exploiting S-Procedure, we show that these robust optimization problems can be formulated into semidefinite programming (SDP). Simulation results have been provided to validate the convergence and the performance of the alternating algorithm.

关键词： Physical-layer secrecy MIMO wiretap channel alternating algorithm convex optimization

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Outage Analysis of Spectrum Sharing Over M-Block Fading With Sensing Information

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IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY 2017年第4期66卷 3071-3087页

作者： Alabbasi, Abdulrahman Rezki, Zouheir Shihada, Basem King Abdullah Univ Sci & Technol Comp Elect & Math Sci & Engn Div Thuwal 23955 Saudi Arabia Royal Inst Technol KTH S-11428 Stockholm Sweden King Abdullah Univ Sci & Technol Dept Elect Engn Thuwal 23955 Saudi Arabia Univ Idaho Moscow ID 83844 USA

Future wireless technologies, such as fifth-generation (5G), are expected to support real-time applications with high data throughput, e.g., holographic meetings. From a bandwidth perspective, cognitive radio (CR) is a promising technology to enhance the system's throughput via sharing the licensed spectrum. From a delay perspective, it is well known that increasing the number of decoding blocks will improve system robustness against errors while increasing delay. Therefore, optimally allocating the resources to determine the tradeoff of tuning the length of the decoding blocks while sharing the spectrum is a critical challenge for future wireless systems. In this paper, we minimize the targeted outage probability over the block-fading channels while utilizing the spectrum-sharing concept. The secondary user's outage region and the corresponding optimal power are derived, over two-block and M-block fading channels. We propose two suboptimal power strategies and derive the associated asymptotic lower and upper bounds on the outage probability with tractable expressions. These bounds allow us to derive the exact diversity order of the secondary user's outage probability. To further enhance the system's performance, we also investigate the impact of including the sensing information on the outage problem. The outage problem is then solved via proposing an alternating optimization algorithm, which utilizes the verified strict quasi-convex structure of the problem. Selected numerical results are presented to characterize the system's behavior and show the improvements of several sharing concepts.

关键词： alternating algorithm block-fading (BF) channel outage probability resource allocation spectrum sensing spectrum sharing

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Robustly Stable Signal Recovery in Compressed Sensing With Structured Matrix Perturbation

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IEEE TRANSACTIONS ON SIGNAL PROCESSING 2012年第9期60卷 4658-4671页

作者： Yang, Zai Zhang, Cishen Xie, Lihua Nanyang Technol Univ Sch Elect & Elect Engn Ctr E City EXQUISITUS Singapore 639798 Singapore Swinburne Univ Technol Fac Engn & Ind Sci Hawthorn Vic 3122 Australia

The sparse signal recovery in the standard compressed sensing (CS) problem requires that the sensing matrix be known a priori. Such an ideal assumption may not be met in practical applications where various errors and fluctuations exist in the sensing instruments. This paper considers the problem of compressed sensing subject to a structured perturbation in the sensing matrix. Under mild conditions, it is shown that a sparse signal can be recovered by l(1) minimization and the recovery error is at most proportional to the measurement noise level, which is similar to the standard CS result. In the special noise free case, the recovery is exact provided that the signal is sufficiently sparse with respect to the perturbation level. The formulated structured sensing matrix perturbation is applicable to the direction of arrival estimation problem, so has practical relevance. algorithms are proposed to implement the l(1) minimization problem and numerical simulations are carried out to verify the results obtained.

关键词： alternating algorithm compressed sensing direction of arrival estimation stable signal recovery structured matrix perturbation

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Global optimization in any minkowski metric: A permutation-translation simulated annealing algorithm for multidimensional scaling

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JOURNAL OF CLASSIFICATION 2007年第2期24卷 277-301页

作者： Vera, J. Fernando Heiser, Willem J. Murillo, Alex Univ Granada Fac Sci Dept Stat & OR E-18071 Granada Spain Leiden Univ Fac Social & Behav Sci Dept Psychol NL-2300 RA Leiden Netherlands Univ Costa Rica Atlantic Branch Turrialba Costa Rica

It is well known that considering a non-Euclidean Minkowski metric in Multidimensional Scaling, either for the distance model or for the loss function, increases the computational problem of local minima considerably. In this paper, we propose an algorithm in which both the loss function and the composition rule can be considered in any Minkowski metric, using a multivariate randomly alternating Simulated Annealing procedure with permutation and translation phases. The algorithm has been implemented in Fortran and tested over classical and simulated data matrices with sizes up to 200 objects. A study has been carried out with some of the common loss functions to determine the most suitable values for the main parameters. The experimental results confirm the theoretical expectation that Simulated Annealing is a suitable strategy to deal by itself with the optimization problems in Multidimensional Scaling, in particular for City-Block, Euclidean and Infinity metrics.

关键词： multidimensional scaling simulated annealing alternating algorithm generallized stress permutation translation Minkowski metric attraction rates

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A symplectic analytical approach for thermal-metallurgical coupling problems: A case study of hot-rolled coil cooling

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2024年 223卷

作者： Wu, Hao Sun, Jie Peng, Wen Jin, Lei Zhang, Dianhua Northeastern Univ State Key Lab Rolling & Automat Shenyang 110819 Peoples R China Shenyang Res Inst Foundry Co Ltd Natl Key Lab Adv Casting Technol CAM Shenyang 110022 Peoples R China

The cooling process of hot-rolled coil directly affects the mechanical and metallurgical properties of the final product. The non -uniform behavior of temperature and microstructure can easily result in sufficient residual stress to induce subsequent cutting deformation. Therefore, the focus of this study is to analyze the thermalmetallurgical coupling problem during the cooling process of hot-rolled coil. Unlike before, a symplectic analytical approach is proposed to calculate the temperature and microstructure evolution of hot-rolled coil. Firstly, the hot-rolled coil is discretized to convert the three-dimensional heat transfer problem in cylindrical coordinate system to cartesian coordinate system. Then, the traditional heat transfer model is introduced into the symplectic Hamiltonian system and the symplectic superposition method is employed to handle complex cooling boundary conditions. The symplectic analytical solution of the three-dimensional temperature field is obtained through rigorous derivation without any assumptions or predetermined solution forms. Meanwhile, an alternating algorithm is designed between the heat transfer model and the phase transformation dynamics model to realize the coupling process. Moreover, a high-precision finite element model verified by the measured data is established. The symplectic analytical solution of coil temperature and microstructure during the cooling process is in good agreement with the finite element solution. Finally, the symplectic approach has been proven to enable quantitative mathematical analysis of the coupling mechanism of thermal-metallurgical processes.

关键词： Symplectic analytical approach Thermal-metallurgical coupling problems Hot-rolled coil Heat transfer alternating algorithm

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