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A regularized smoothing newton-type algorithm for quasi-variational inequalities

COMPUTERS & MATHEMATICS WITH APPLICATIONS 2014年第10期68卷 1312-1324页

作者： Ni, Tie Zhai, Jun Liaoning Tech Univ Coll Business Adm Huludao 125105 Peoples R China Univ Chicago Dept Math Chicago IL 60615 USA

This paper is concerned with developing an efficient regularized smoothing newton-type algorithm for quasi-variational inequalities. The proposed algorithm takes the advantage of newly introduced smoothing functions and a non-monotone line search strategy. It is proved to be globally and locally superlinearly/quadratically convergent under suitable assumptions. Numerical results demonstrate that the algorithm generally outperforms the existing interior point method and semismooth method (Facchinei, et al. 2014). (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Quasi-variational inequality Non-monotone line search newton-type algorithm Smoothing function Global convergence Superlinear/quadratic convergence

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Smart application for inter-area oscillations monitoring based on newton-type algorithm

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2016年第11期26卷 2370-2384页

作者： Cai, Deyu Regulski, Pawel Terzija, Vladimir Shanghai Elect Power Corp Ltd Tower 1Resource Plaza268 Zhongshan Rd S Shanghai 200010 Peoples R China Univ Manchester Elect & Elect Engn Manchester M13 9PL Lancs England

A new Wide-Area Monitoring System (WAMS) application for monitoring inter-area oscillations, based on the newton-type algorithm is presented in this paper. The core of this novel WAMS application is a numerical algorithm for the real-time estimation of the dominant inter-area oscillation mode, which processes Global Positioning System synchronized information obtained from Phasor Measurement Units installed in the power system. The parameter model is a highly nonlinear function, making this a particularly difficult challenge. Two data sets were tested using the new algorithm, one based on simulated models and the other based on real-life data records. The computer simulated model was based on a known architecture with signals obtained using a dynamic simulation of a multi-machine power system. The real-life data records used information collected on the FlexNet Wide-Area Monitoring System (FlexNET-WAMS) installed in the Great Britain power grid. Copyright (c) 2016 John Wiley & Sons, Ltd.

关键词： nonlinear parameter estimation newton-type algorithm power systems inter-area oscillations Wide-Area Monitoring Systems

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Efficient regularized newton-type algorithm for solving convex optimization problem

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JOURNAL OF APPLIED MATHEMATICS AND COMPUTING 2022年第4期68卷 2343-2363页

作者： Javed, Shazia Khan, Areeba Lahore Coll Women Univ Dept Math Lahore 54000 Pakistan

In this paper, the subspace properties of trust-region methods are employed to develop a regularized newton-type (RNT) algorithm for solving convex optimization problem. The proposed RNT algorithm is analyzed for quadratic convergence under the local error bound conditions and global convergence for unconstrained convex optimization problems which may have singular Hessian at the solutions. Afterwards numerical results are presented to show the efficiency and robustness of the proposed algorithm in producing an optimal solution for the given problem.

关键词： Convex optimization Regularization factor trust-region newton-type algorithm

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A newton-type algorithm for generalized linear complementarity problem over a polyhedral cone

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APPLIED MATHEMATICS AND COMPUTATION 2005年第1期169卷 388-401页

作者： Zhang, XZ Ma, FM Wang, YJ Qufu Normal Univ Inst Operat Res Rizhao Shandong 276800 Peoples R China Qufu Normal Univ Dept Math Qufu 273165 Peoples R China

in this paper, the generalized linear complementarity problem over a polyhedral cone (GLCP) is reformulated as an unconstrained optimization, based on which we propose a newton-type algorithm to solve it. Under certain conditions, we show that the algorithrn converges globally and quadratically. Preliminary numerical experiments are also reported in this paper. (c) 2004 Elsevier Inc. All rights reserved.

关键词： GLCP optimization reformulation newton-type algorithm

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Development of newton-type adaptive algorithm for minimization of EOG artefacts from noisy EEG signals

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SIGNAL PROCESSING 1997年第2期62卷 173-186页

作者： Sadasivan, PK Dutt, DN McMaster Univ Commun Res Lab Hamilton ON L8S 4K1 Canada

In this paper, we propose an adaptive algorithm using newton's method for the enhancement of EEG signals in the presence of EOG artefacts. We consider two models for the noise (i.e., artefacts) estimation: (i) the conventional linear model and (ii) a nonlinear model using second-order Volterra function. Application of newton's method to the linear case results in the conventional recursive least-squares algorithm. Since the parameters of the nonlinear model are specified in terms of a vector and a matrix, the conventional newton's method could not be applied. Hence, the underlying cost function has been reformulated whereby all the parameters are represented by a single vector and then newton's method is applied to this reformulated cost function. While developing the algorithm for the nonlinear case, the Hessian matrix is approximated because of the special property of the reference signal. This ensures the reduced computational complexity and positive definiteness of the approximated Hessian so as to ensure search along the descent directions. Another algorithm making use of the exact Hessian matrix is also derived. These algorithms were used to minimize the EOG artefacts from EEG signals. Simulation results show that the nonlinear scheme with approximated Hessian works well compared to the other two algorithms in minimizing EOG artefacts from contaminated EEG signals. (C) 1997 Published by Elsevier Science B.V.

关键词： newton-type algorithm adaptive minimization nonlinear modeling Hessian electroencephalogram EOG artefacts noise reduction

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Symmetrical components estimation through nonrecursive newton-type numerical algorithm

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IEEE TRANSACTIONS ON POWER DELIVERY 2003年第2期18卷 359-363页

作者： Terzija, VV Markovic, D Univ Belgrade Fac Elect Engn Belgrade Serbia Elektromorava YU-12000 Pozarevac Serbia

The paper reports new software developments for symmetrical components estimation. Nonrecursive newton-type algorithm is extended with the second stage algorithm for symmetrical components calculation from the estimated fundamental phasors of three-phase signals (arbitrary voltages or currents). The algorithm is not sensitive to power system frequency changes and to the harmonic distortion of input signals. The algorithm is tested through computer simulations and by using laboratory obtained input signals and those recorded in the real distribution network.

关键词： newton-type algorithm nonlinear estimation numerical algorithm symmetrical components

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A fast approximate algorithm for training L₁-SVMs in primal space

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NEUROCOMPUTING 2007年第7-9期70卷 1554-1560页

作者： Wang, Lei Sun, Shixin Zhang, Kai Univ Elect Sci & Technol China Sch Comp Sci & Engn Chengdu 610054 Peoples R China Florida State Univ Coll Engn CISCOR Tallahassee FL 32310 USA

We propose a novel and fast algorithm to train support vector machines (SVMs) in primal space, which solves an approximate optimization of SVMs with the properties of unconstraint, continuity and twice differentiability by utilizing the newton optimization technique. Further, we devise a special pre-extracting procedure to speed up the convergence of the algorithm by resorting to a high-quality initial solution. Theoretical studies show that the proposed algorithm produces an e-approximate solution to standard SVMs and maintains low computational complexity. Experimental results on benchmark data sets demonstrate that our algorithm is much faster than the dual based method such as SVMlight while it achieves the similar test accuracy. (c) 2006 Elsevier B.V. All rights reserved.

关键词： support vector machines primal optimization Huber regression function newton-type algorithm

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Penalized maximum likelihood inference under the mixture cure model in sparse data

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STATISTICS IN MEDICINE 2023年第13期42卷 2134-2161页

作者： Xu, Changchang Bull, Shelley B. Univ Toronto Dalla Lana Sch Publ Hlth Div Biostat 155 Coll St Toronto ON M5T3M7 Canada Lunenfeld Tanenbaum Res Inst Sinai Hlth 60 Murray St Toronto ON M5T3L9 Canada

Introduction: When a study sample includes a large proportion of long-term survivors, mixture cure (MC) models that separately assess biomarker associations with long-term recurrence-free survival and time to disease recurrence are preferred to proportional-hazards models. However, in samples with few recurrences, standard maximum likelihood can be *** and Methods: We extend Firth-type penalized likelihood (FT-PL) developed for bias reduction in the exponential family to the Weibull-logistic MC, using the Jeffreys invariant prior. Via simulation studies based on a motivating cohort study, we compare parameter estimates of the FT-PL method to those by ML, as well as type 1 error (T1E) and power obtained using likelihood ratio ***: In samples with relatively few events, the Firth-type penalized likelihood estimates (FT-PLEs) have mean bias closer to zero and smaller mean squared error than maximum likelihood estimates (MLEs), and can be obtained in samples where the MLEs are infinite. Under similar T1E rates, FT-PL consistently exhibits higher statistical power than ML in samples with few events. In addition, we compare FT-PL estimation with two other penalization methods (a log-F prior method and a modified Firth-type method) based on the same ***: Consistent with findings for logistic and Cox regressions, FT-PL under MC regression yields finite estimates under stringent conditions, and better bias-and-variance balance than the other two penalizations. The practicality and strength of FT-PL for MC analysis is illustrated in a cohort study of breast cancer prognosis with long-term follow-up for recurrence-free survival.

关键词： Firth-type penalized likelihood likelihood ratio test maximum likelihood mixture cure nested deviance method newton-type algorithm

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Computational issues in parameter estimation for stationary hidden Markov models

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COMPUTATIONAL STATISTICS 2008年第1期23卷 1-18页

作者： Bulla, Jan Berzel, Andreas Univ Gottingen Inst Stat & Econometr Ctr Stat D-37073 Gottingen Germany

The parameters of a hidden Markov model (HMM) can be estimated by numerical maximization of the log-likelihood function or, more popularly, using the expectation-maximization (EM) algorithm. In its standard implementation the latter is unsuitable for fitting stationary hidden Markov models (HMMs). We show how it can be modified to achieve this. We propose a hybrid algorithm that is designed to combine the advantageous features of the two algorithms and compare the performance of the three algorithms using simulated data from a designed experiment, and a real data set. The properties investigated are speed of convergence, stability, dependence on initial values, different parameterizations. We also describe the results of an experiment to assess the true coverage probability of bootstrap-based confidence intervals for the parameters.

关键词： computational methods confidence intervals EM algorithm hybrid algorithm initial conditions newton-type algorithm parameterization stationary hidden Markov model

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Training One-class Support Vector Machines in the Primal Space

Training One-class Support Vector Machines in the Primal Spa...

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International Conference on Electronic Computer Technology

作者： Wang, Lei Yang, Yong Southwestern Univ Finance & Econ Sch Econ Informat Engn Chengdu 610074 Peoples R China Suminet Commun Technol Co Ltd Shanghai 200127 Peoples R China

ISBN: (纸本)9780769535593

In this paper, we proposed a novel newton-type solver for one-class support vector machines in the primal space directly. Firstly, utilizing reproducing property of kernel and Huber regression function, original constrained quadratic programming is transformed into approximate unconstrained one, which is continuous and twice differentiable. Then, we give a newton-type training algorithm to solve it. Further analysis shows the computation complexity of our algorithm is identical with theoretical lower bound for solving one-class support vector machines. In the end, experiments on 9 UCI datasets are done to validate the effectivity of proposed algorithm, and when comparing with dual method (LIBSVM), its produces comparative testing accuracy, better training speed, and less support vectors.

关键词： one-class support vector machines primal space newton-type algorithm

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