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Affine projection Algorithm for Censored Regression

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS II-EXPRESS BRIEFS 2021年第12期68卷 3602-3606页

作者： Zhao, Haiquan Zhao, Feng Wang, Gen Zhou, Lijun Song, Pucha Southwest Jiaotong Univ Key Lab Magnet Suspens Technol & Maglev Vehicle Minist Educ Chengdu 610031 Peoples R China Southwest Jiaotong Univ Sch Elect Engn Chengdu 610031 Peoples R China

Non-Gaussian colored input signal and censored observation are encountered frequently in many practical applications of adaptive signal processing. Conventional adaptive algorithms will face convergence performance degradation in such cases. To address the issue, the affine projection algorithm for censored regression (CR-APA) is proposed in this brief. The censored thresholds and the variance of the background noise are regarded as the prior knowledge to compensate for the bias caused by censored observation. By theoretical analysis, the range of the step size is derived to guarantee the stabilization of the CR-APA. Besides, the method of evolving projection order is employed to improve the convergence performance of the CR-APA. Computer simulations in system identification and echo cancellation applications are performed to demonstrate the better convergence performance of the proposed algorithms in censored data processing over competing algorithms, and to verify the improvement of the CR-APA by the method of evolving projection order. The proposed CR-APA and CR-EAPA can be used in engineering applications to make up for the hardware.

关键词： Signal processing algorithms Convergence Adaptation models Computational modeling projection algorithms Noise measurement System identification Censored regression affine projection algorithm adaptive filter evolving order

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ON THE POSSIBLE DIVERGENCE OF THE projection ALGORITHM

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1995年第3期40卷 495-497页

作者： LEFEBER, E POLDERMAN, JW Department of Applied Mathematics University of Twente Enschede Netherlands Universiteit Twente Enschede Overijssel NL Dept. of Appl. Math. Twente Univ. Enschede Netherlands

It is shown by means of an example that the projection algorithm does not always converge.

关键词： projection algorithms State estimation Power system modeling Parameter estimation Convergence Signal processing Concurrent computing Distributed computing Computer aided analysis Electronic circuits

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GRADIENT projection ALGORITHM FOR MULTIPLE ROUTING IN MESSAGE-SWITCHED NETWORKS

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IEEE TRANSACTIONS ON COMMUNICATIONS 1976年第4期24卷 449-456页

作者： SCHWARTZ, M CHEUNG, CK COLUMBIA UNIV DEPT ELECT ENGN & COMP SCINEW YORKNY 10027 GE ROCKVILLEMD

Various algorithms have been proposed for determining the routing paths designed to minimize the average overall message time delay in message-switched networks. In this paper we describe the application of the gradient projection algorithm to this problem. This algorithm is a gradient-type search procedure designed to handle constrained optimization problems, into which category the routing problem falls. Calculations of the computational complexity of this algorithm indicate that it is particularly well-suited to networks with a limited number of commodities or source-destination pairs. The algorithm is applied to a representative group of distributed-type networks, of varying complexity. Execution times for this algorithm are compared with those obtained using the flow deviation routing algorithm. These agree roughly with the results of the computational requirement calculations; i.e., this algorithm generally requires less execution time for networks with a relatively small number of commodities than does the flow deviation method. (The actual running time depends significantly on the choice of the initial flows or routing paths, however.) For those networks in which all network nodes may be expected to communicate with all other nodes, however, the flow deviation method would be expected to be superior.

关键词： projection algorithms Routing Delay effects Algorithm design and analysis Computer networks Buffer storage Queueing analysis Constraint optimization Design optimization Computational complexity

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projection methods for conic feasibility problems: applications to polynomial sum-of-squares decompositions

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OPTIMIZATION METHODS & SOFTWARE 2011年第1期26卷 23-46页

作者： Henrion, Didier Malick, Jerome Univ Toulouse CNRS LAAS Toulouse France Czech Tech Univ Fac Elect Engn CR-16635 Prague Czech Republic Univ Grenoble CNRS Lab Jean Kuntzmann Grenoble France

This paper presents a projection-based approach for solving conic feasibility problems. To find a point in the intersection of a cone and an affine subspace, we simply project a point onto this intersection. This projection is computed by dual algorithms operating a sequence of projections onto the cone and generalizing the alternating projection method. We release an easy-to-use Matlab package implementing an elementary dual-projection algorithm. Numerical experiments show that, for solving some semidefinite feasibility problems, the package is competitive with sophisticated conic programming software. We also provide a particular treatment for semidefinite feasibility problems modelling polynomial sum-of-squares decomposition problems.

关键词： convex cones semidefinite programming projection algorithms positive polynomials least-squares problems

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ON THE projection ALGORITHM AND DELAY OF PEAKING IN ADAPTIVE-CONTROL

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IEEE TRANSACTIONS ON AUTOMATIC CONTROL 1993年第4期38卷 581-584页

作者： DELYON, B IZMAILOV, R JUDITSKY, A MOSCOW INFORMAT TRANSMISS PROBLEMS INST MOSCOW 101447RUSSIA

Adaptive deadbeat control is considered for the deterministic linear plant without any persistent excitation assumption imposed. The upper bound on the rate of convergence is provided for the control algorithm that uses the projection identification algorithm. On the other hand, we show that convergence is delayed if the ''regularized'' identification algorithm is used. It is shown that arbitrarily large delays can precede an overshoot under certain choices of initial conditions. An estimate is also provided for the amplitude of the peak.

关键词： projection algorithms Delay Adaptive control Convergence Control systems Upper bound Amplitude estimation Equations Parameter estimation

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A Randomized Algorithm for Generalized Accelerated projection Method

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IEEE CONTROL SYSTEMS LETTERS 2021年第1期5卷 85-90页

作者： Qin, Tiancheng Etesami, S. Rasoul Univ Illinois Dept Ind & Enterprise Syst Engn Urbana IL 61801 USA

We consider the convex feasibility problem, which is to determine a point in the intersection of a finite number of closed convex sets. It was shown in the past literature a so-called generalized acceleration method converges to a feasible point in the intersection of all the sets, assuming the intersection set has a nonempty interior. In this letter, we establish the same convergence result without any assumption on the interior of the feasible set. In particular, we devise a randomized accelerated projection algorithm and prove its linear convergence rate when all the convex sets are half-spaces in a finite-dimensional Euclidean space. Numerical experiments comparing the generalized acceleration method with the classic cyclic projection methods are presented, which justify the fast convergence rate and the out-performance of the proposed algorithm.

关键词： Acceleration Convergence projection algorithms Convex functions Iterative methods Indexes Optimal control Successive projection method convex feasibility convex optimization

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Low Cost Variable Step-Size LMS With Maximum Similarity to the Affine projection Algorithm

IEEE OPEN JOURNAL OF SIGNAL PROCESSING

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IEEE OPEN JOURNAL OF SIGNAL PROCESSING 2024年 5卷 82-91页

作者： Ferrer, Miguel De Diego, Maria Gonzalez, Alberto Univ Politecn Valencia UPV Inst Telecommun & Multimedia Applicat iTEAM Valencia 46022 Spain

The LMS algorithm is widely employed in adaptive systems due to its robustness, simplicity, and reasonable performance. However, it is well known that this algorithm suffers from a slow convergence speed when dealing with colored reference signals. Numerous variants and alternative algorithms have been proposed to address this issue, though all of them entail an increase in computational cost. Among the proposed alternatives, the affine projection algorithm stands out. This algorithm has the peculiarity of starting from $N$ data vectors of the reference signal. It transforms these vectors into as many data vectors suitably normalized in energy and mutually orthogonal. In this work, we propose a version of the LMS algorithm that, similar to the affine projection algorithm, starts from $N$ data vectors of the reference signal but corrects them by using only a scalar factor that functions as a convergence step. Our goal is to align the behavior of this algorithm with the behavior of the affine projection algorithm without significantly increasing the computational cost of the LMS.

关键词： Signal processing algorithms Convergence projection algorithms Computational efficiency Approximation algorithms Costs Robustness Adaptive filters affine projection algorithm variable step-size

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THE GENERALIZED BACK projection THEOREM FOR CONE BEAM RECONSTRUCTION

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IEEE TRANSACTIONS ON NUCLEAR SCIENCE 1985年第4期32卷 1512-1519页

作者： PEYRIN, FC Laboratoire de Traitement du Signal et Ultrasons INSA Villeurbanne France

The use of cone beam scanners raises the problem of three dimensional reconstruction from divergent projections. After a survey on bidimensional analytical reconstruction methods we examine their application to the 3D problem. Finally, it is shown that the back projection theorem can be generalized to cone beam projections. This allows to state a new inversion formula suitable for both the 4 π parallel and divergent geometries. It leads to the generalization of the "rho-filtered back projection " algorithm which is outlined.

关键词： Image reconstruction Back Geometry projection algorithms Computed tomography Convolution Reconstruction algorithms Diagnostic radiography Biomedical imaging Spatial resolution

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A New projection Algorithm for Generalized Variational Inequality

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JOURNAL OF INEQUALITIES AND APPLICATIONS 2010年第1期2010卷 182576-182576页

作者： Fang, Changjie He, Yiran Sichuan Normal Univ Dept Math Chengdu 610068 Sichuan Peoples R China Chongqing Univ Posts & Telecommun Inst Appl Math Chongqing 400065 Peoples R China

We propose a new projection algorithm for generalized variational inequality with multivalued mapping. Our method is proven to be globally convergent to a solution of the variational inequality problem, provided that the multivalued mapping is continuous and pseudomonotone with nonempty compact convex values. Preliminary computational experience is also reported.

关键词： projection algorithms Multivalued inequalities MAPPING(MATHEMATICAL)

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An inertial-double-projection-based algorithm for large-scale nonlinear systems of monotone equations

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NUMERICAL algorithms 2024年 1-20页

作者： Barari, Suma Amini, Keyvan Kamandi, Ahmad Razi Univ Fac Sci Dept Math Kermanshah Iran Univ Sci & Technol Mazandran Fac Sci Dept Math Behshahr Mazandran Iran

In this paper, we propose a derivative-free algorithm for solving large-scale nonlinear systems of monotone equations. This algorithm incorporates a pivotal step inspired by double projection methods, which is further refined through an inertial approach to approximate the solution more effectively. The global convergence of the new algorithm is investigated under some mild conditions. The results of some numerical tests, along with their performance profiles, demonstrate the algorithm's efficacy.

关键词： Iterative methods Nonlinear equations Monotone equations Derivative free methods projection algorithms

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