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Global convergence and ascent property of a cyclic algorithm used for statistical analysis of crash data

Afrika Statistika 2018年第2期13卷 1631-1643页

作者： Issa Cherif Geraldo Assi N'Gessan Kossi Essona Gneyou

In this paper, we consider an estimation algorithm called cyclic iterative algorithm (CA) that is used in statistics to estimate the unknown vector parameter of a crash data model. We provide a theoretical proof of the global convergence of the CA that justifies the good numerical results obtained in early numerical studies of this algorithm. We also prove that the CA is an ascent algorithm, what ensures its numerical stability. Dans cet article, nous considérons un algorithme d'estimation appelé algorithme cyclic iteratif (CA) utilisé en statistique pour estimer le vecteur paramètre inconnu d'une modèle pour les données d'accidents. Nous donnons une preuve th'eorique de la convergence globale du CA qui justifie les excellents résultats numériques obtenues dans les études numériques antérieures dudit algorithme. Nous prouvons aussi que le CA augmente la log-vraisemblance à chaque itération, ce qui assure sa stabilité numérique.

关键词： 62-04 62F10 62H12 62P99 cyclic algorithm global convergence iterative method maximum likelihood road safety

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A cyclic algorithm for maximum likelihood estimation using Schur complement

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NUMERICAL LINEAR ALGEBRA WITH APPLICATIONS 2015年第6期22卷 1161-1179页

作者： N'Guessan, Assi Geraldo, Issa Cherif Univ Lille 1 UMR CNRS 8524 Lab Paul Painleve F-59655 Villeneuve Dascq France UCAO UUT Dept Math & Informat Lome Togo

Using the Schur complement of a matrix, we propose a computational framework for performing constrained maximum likelihood estimation in which the unknown parameters can be partitioned into two sets. Under appropriate regularity conditions, the corresponding estimating equations form a non-linear system of equations with constraints. Solving this system is typically accomplished via methods which require computing or estimating a Hessian matrix. We present an alternative algorithm that solves the constrained non-linear system in block coordinate descent fashion. An explicit form for the solution is given. The overall algorithm is shown in numerical studies to be faster than standard methods that either compute or approximate the Hessian as well as the classical Nelder-Mead algorithm. We apply our approach to a motivating problem of evaluating the effectiveness of Road Safety Policies. This includes several numerical studies on simulated data. Copyright (C) 2015 John Wiley & Sons, Ltd.

关键词： Schur complement constrained optimization maximum likelihood cyclic algorithm road safety measure simulation

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Optimal Mismatched Filter Design by Combining Convex Optimization With Circular algorithm

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IEEE ACCESS 2022年 10卷 56763-56772页

作者： Jin, Ling Wang, Ju Zhong, Yi Wang, Duo Beijing Inst Technol Sch Informat & Elect Beijing 100081 Peoples R China

Mismatched filters (MMF) have been intensively explored for linear-frequency modulation (LFM) waveform sidelobe reduction. Unlike other design strategies, the use of convex optimization (CO) techniques is able to find the optimal design. However, existing studies for CO-based MMF design have focused on minimizing peak sidelobe level (PSL), which might not take the mainlobe widening sacrifice into account. To address this issue, this paper proposes a weighted CO model targeting a flexible tradeoff between sidelobe suppression and mainlobe widening. Moreover, to better control the optimization problem via the presented CO model, the cyclic algorithm (CA) is employed to determine upper limits on mainlobe width. Consequently, the proposed tradeoff MMF design by combining CA with CO would be feasible to meet the requirements of different target detection scenarios. Comprehensive simulations have been carried out to demonstrate the effectiveness of our presented MMF design.

关键词： Signal to noise ratio Optimization Radar Object detection Licenses Design methodology Convex functions Mismatched filter convex optimization cyclic algorithm sidelobe suppression

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Designing Sequences With Minimized Mean Sidelobe Level for Cognitive Radars

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IEEE ACCESS 2021年 9卷 101643-101654页

作者： Najafabadi, Hamid Esmaeili Leung, Henry Moo, Peter W. Univ Calgary Dept Elect & Comp Engn Calgary AB T2N 1N4 Canada Def Res & Dev Canada Radar Sensing & Exploitat Sect Ottawa ON K1A 0Z4 Canada

In this paper, a set of sequences is developed with a minimized mean sidelobe level (MSL). The problem is formulated for cognitive radars using the l(1)-norm, where the target cognition determines which sidelobes should be suppressed. The cognitive radar configuration requires fast waveform regeneration in each cognition cycle. In this light, the computational burden of the algorithms developed here is revealed to be situated on the singular value decomposition (SVD) operation. The randomization method is adopted to speed up the proposed algorithms. The obtained fast generation of sequences with the desired autocorrelation is key to its utilization in cognitive radars. We also consider two practically important cases and accommodate the proposed approach to them: unimodular and finite-alphabet sequences. The superiority of the developed algorithms is confirmed both in suppression level and speed through extensive numerical simulations.

关键词： Correlation Cognition Cognitive radar Minimization Measurement Signal processing algorithms Optimization cyclic algorithm cognitive radar mean sidelobe level radar waveform design

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Linear convergence of the generalized Douglas-Rachford algorithm for feasibility problems

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JOURNAL OF GLOBAL OPTIMIZATION 2018年第3期72卷 443-474页

作者： Dao, Minh N. Phan, Hung M. Univ Newcastle CARMA Callaghan NSW 2308 Australia Univ Massachusetts Kennedy Coll Sci Dept Math Sci Lowell MA 01854 USA

In this paper, we study the generalized Douglas-Rachford algorithm and its cyclic variants which include many projection-type methods such as the classical Douglas-Rachford algorithm and the alternating projection algorithm. Specifically, we establish several local linear convergence results for the algorithm in solving feasibility problems with finitely many closed possibly nonconvex sets under different assumptions. Our findings not only relax some regularity conditions but also improve linear convergence rates in the literature. In the presence of convexity, the linear convergence is global.

关键词： Affine-hull regularity cyclic algorithm Generalized Douglas-Rachford algorithm Linear convergence Linear regularity Strong regularity Superregularity Quasi Fejer monotonicity Quasi coercivity

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Prior Knowledge Based Transmit Nulling Method for MIMO Radar

Prior Knowledge Based Transmit Nulling Method for MIMO Radar

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International Conference on Radar (RADAR)

作者： Zheng, Hao Jiu, Bo Liu, Hongwei Liu, Yuan Wang, Xu Xidian Univ Natl Lab Radar Signal Proc Xian Shaanxi Peoples R China Xian Elect Engn Res Inst Xian Shaanxi Peoples R China

ISBN: (纸本)9781538672174

In this paper, a multiple-input-multiple-output (MIMO) radar transmit nulling method is proposed in the presence of fast moving interference. The MIMO radar transmit waveform design is divided into two steps: transmit waveform covariance matrix optimization and transmit waveform synthesis to approximate the optimized covariance matrix. In the first step, the prior knowledge of interference is utilized to optimize covariance matrix and the derivative constraint is introduced to widen nulls. In the second step, most existing methods, e.g. cyclic algorithm (CA) and sequential iterative algorithm (SIA), synthesize the waveform with constant modulus under least-squares criterion. As the value at the null even can be neglected in the calculation of least-squares, these methods cannot form deep enough nulls at the interference direction. Aiming at this problem, a block coordinate descent (BCD) method is proposed to optimize the initial waveform synthesized by CA. Besides, the optimized waveform is still constant modulus. Numerical results show the efficiency of the proposed method.

关键词： MIMO radar transmit nulling interference cyclic algorithm block coordinate descent constant modulus waveform

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About One Approach to Robot Control System Simulation 1

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3rd International Conference on Interactive Collaborative Robotics (ICR)

作者： Larkin, Eugene Bogomolov, Alexey Privalov, Aleksandr Antonov, Maksim Tula State Univ Tula 300012 Russia Tula State Pedag Univ Tula 300026 Russia

ISBN: (数字)9783319995823

ISBN: (纸本)9783319995823;9783319995816

Mobile robot onboard equipment functioning is considered. It is shown, that abstract analogue of one equipment unit operation is an ordinary semi-Markov process. This abstraction is insufficient for analytical modeling the mobile robot as a whole, so to simulate synchronized onboard equipment functioning, it is necessary to use more complicated abstraction based on integration of ordinary processes to so-called M-parallel semi-Markov process. For definition of such abstraction notification "functional states" as combinations of structural states is introduced. Method of definition of semi-Markov matrix parameters, such as time of residence in functional states and probabilities of switches from current functional states to neighboring functional states is proposed. Theoretical result is confirmed by modeling of homogeneous system, every unit of which may resident in "on" of "off" state.

关键词： Mobile robot cyclic algorithm Structural state Functional state semi-Markov process

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Range Sidelobes Attenuation of Pseudorandom Waveforms for Civil Radars 14

Range Sidelobes Attenuation of Pseudorandom Waveforms for Ci...

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14th European Radar Conference (EURAD)

作者： De Palo, Francesco Galati, Gaspare Tor Vergata Univ Dept Elect Engn Rome Italy

ISBN: (纸本)9782874870491

In the last years the solid state technology is entering the marine market with some new coherent radars with solid-state transmitters. They are characterized by a full-digital signal processing making use of FPGA boards that make the whole system very flexible. Solid-state transmitters require pulse-compression and a matched-filter receiver calling for waveforms with a low level of range sidelobes. This need has been addressed in the past with the well-known chirp, or Frequency-Modulated signals with a suited non linear frequency law allowing very low autocorrelation sidelobes. But nowadays a different approach is possible thanks to the Noise Radar Technology that uses tailored-at-will noise signals for the medium-long range detection. The tailoring of such signals is implemented by novel, suitable algorithms depending on the particolar application. In this paper a new powerful cyclic algorithm (BLASA) is presented which is able to strongly attenuate the range sidelobes of noisy signals while keeping their bandwidth within given bounds. In this paper, particular focus is given to the marine radar environment in which pulses of different duration are used.

关键词： Solid-state radars Range sidelobes suppression Noise Radar Technology cyclic algorithm Marine radar

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Parallel and cyclic hybrid subgradient extragradient methods for variational inequalities

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AFRIKA MATEMATIKA 2017年第5-6期28卷 677-692页

作者： Dang Van Hieu Vietnam Natl Univ Dept Math 334 Nguyen Trai St Hanoi Vietnam

In this paper, we propose two hybrid subgradient extragradient methods for solving common solutions of variational inequalities problems (CSVIP). The first is a parallel algorithm which can be performed simultaneously while the second is a cyclic algorithm which is computed sequentially on each subproblem in the family. The novelty of this paper is that we have designed the algorithms to develop possible practical numerical methods when the number of subproblems is large. The algorithms can be considered as improvements of some previously known results for CSVIPs. Numerical experiments are also performed to illustrate the efficiency of the proposed algorithms.

关键词： Hybrid method Subgradient extragradient method Parallel algorithm cyclic algorithm Variational inequality

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Synchronal algorithm and cyclic algorithm for fixed point problems and variational inequality problems in hilbert spaces

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FIXED POINT THEORY AND APPLICATIONS 2011年第1期000卷 1-14页

作者： Tian, Ming Di, Lanyun Civil Aviat Univ China Coll Sci Tianjin 300300 Peoples R China

We design synchronal algorithm and cyclic algorithm based on the general iterative algorithm proposed by Tian in 2010 for finding the common fixed point x* of finite family of strict pseudo- contractive mappings which is the solution of the variational inequality <(gamma f - mu F)x*, x - x*> <= 0, for all x is an element of boolean AND(N)(-=1) F(T(i)).

关键词： strict pseudo-contractions nonexpansive mapping variational inequality synchronal algorithm cyclic algorithm fixed point

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