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Advanced Computational Modeling and Mechanical Behavior Analysis of Multi-Directional Functionally Graded Nanostructures:A Comprehensive Review 认领 引用
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作者 Akash Kumar Gartia S.Chakraverty 《Computer Modeling in Engineering & Sciences》 SCIE EI 2025年第3期2405-2455,共51页
This review explores multi-directional functionally graded(MDFG)nanostructures,focusing on their material characteristics,modeling approaches,and mechanical behavior.It starts by classifying different types of functio... This review explores multi-directional functionally graded(MDFG)nanostructures,focusing on their material characteristics,modeling approaches,and mechanical behavior.It starts by classifying different types of functionally graded(FG)materials such as conventional,axial,bi-directional,and tri-directional,and the material distribution models like power-law,exponential,trigonometric,polynomial functions,etc.It also discusses the application of advanced size-dependent theories like Eringen’s nonlocal elasticity,nonlocal strain gradient,modified couple stress,and consistent couple stress theories,which are essential to predict the behavior of structures at small scales.The review covers the mechanical analysis of MDFG nanostructures in nanobeams,nanopipes,nanoplates,and nanoshells and their dynamic and static responses under different loading conditions.The effect of multi-directional material gradation on stiffness,stability and vibration is discussed.Moreover,the review highlights the need for more advanced analytical,semi-analytical,and numerical methods to solve the complex vibration problems ofMDFG nanostructures.It is evident that the continued development of these methods is crucial for the design,optimization,and real-world application of MDFG nanostructures in advanced engineering fields like aerospace,biomedicine,and microanoelectromechanical systems(MEMS/NEMS).This study is a reference for researchers and engineers working in the domain of MDFG nanostructures. 展开更多
关键词 Functionally graded multi-directional nano size-dependent vibration
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Using mixed kernel support vector machine to improve the predictive accuracy of genome selection 认领 引用 被引量：2
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作者 Jinbu Wang Wencheng Zong +6 位作者 Liangyu Shi Mianyan Li Jia Li Deming Ren Fuping Zhao Lixian Wang Ligang Wang 《Journal of Integrative Agriculture》 SCIE CAS CSCD 2026年第2期775-787,共13页
The advantages of genome selection(GS) in animal and plant breeding are self-evident.Traditional parametric models have disadvantage in better fit the increasingly large sequencing data and capture complex effects acc... The advantages of genome selection(GS) in animal and plant breeding are self-evident.Traditional parametric models have disadvantage in better fit the increasingly large sequencing data and capture complex effects accurately.Machine learning models have demonstrated remarkable potential in addressing these challenges.In this study,we introduced the concept of mixed kernel functions to explore the performance of support vector machine regression(SVR) in GS.Six single kernel functions(SVR_L,SVR_C,SVR_G,SVR_P,SVR_S,SVR_L) and four mixed kernel functions(SVR_GS,SVR_GP,SVR_LS,SVR_LP) were used to predict genome breeding values.The prediction accuracy,mean squared error(MSE) and mean absolute error(MAE) were used as evaluation indicators to compare with two traditional parametric models(GBLUP,BayesB) and two popular machine learning models(RF,KcRR).The results indicate that in most cases,the performance of the mixed kernel function model significantly outperforms that of GBLUP,BayesB and single kernel function.For instance,for T1 in the pig dataset,the predictive accuracy of SVR_GS is improved by 10% compared to GBLUP,and by approximately 4.4 and 18.6% compared to SVR_G and SVR_S respectively.For E1 in the wheat dataset,SVR_GS achieves 13.3% higher prediction accuracy than GBLUP.Among single kernel functions,the Laplacian and Gaussian kernel functions yield similar results,with the Gaussian kernel function performing better.The mixed kernel function notably reduces the MSE and MAE when compared to all single kernel functions.Furthermore,regarding runtime,SVR_GS and SVR_GP mixed kernel functions run approximately three times faster than GBLUP in the pig dataset,with only a slight increase in runtime compared to the single kernel function model.In summary,the mixed kernel function model of SVR demonstrates speed and accuracy competitiveness,and the model such as SVR_GS has important application potential for GS. 展开更多
关键词 genome selection machine learning support vector machine kernel function mixed kernel function
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Structural characterization and immunological function of a neutral polysaccharide from Areca catechu L.kernels 认领 引用
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作者 Jing Zhang Xuejie Feng +4 位作者 Jiahui Dai Shiping Wang Xiaoning Kang Wenting Dai Jianbang Ji 《Tropical Plants》 CSCD 2025年第1期223-235,共13页
Areca nut kernels are the byproduct of areca nut processing.Some of the major bioactive components of the areca nut are polysaccharides.Polysaccharides are known to exert numerous biological activities.Thus,polysaccha... Areca nut kernels are the byproduct of areca nut processing.Some of the major bioactive components of the areca nut are polysaccharides.Polysaccharides are known to exert numerous biological activities.Thus,polysaccharides isolated from areca nut kernels may be clinically valuable.To determine the medicinal value of areca nut kernel polysaccharides(AKP),ultrasonic-assisted extraction,ethanol precipitation,and dialysis were used for separation and purification.SEM,XRD,FTIR,and NMR were used for structural characterization and RAW264.7 macrophages were used for in vitro immune activity assessment.The AKP were isolated was a neutral polysaccharide,and the molecular weight(Mw)was 6.95×105Da,primarily composed of mannose(58.7%)and galactose(33.6%);the main chain of AKP is→4)-β-D-Manp-(1→,and the branched chain was mainly ofα-D-Galp-(1→attached to the O-6 position of→4,6)-β-D-Manp-(1→.Cell experiments show that AKP(20μg/mL)exerts its immune function via the TLR4/NF-κB signaling pathway regulation,decreasing TLR4,P65,IκB-α,and MyD88,and reducing the release of TNF-α,NO,IL-6,and IL-1β.In addition,AKP immune activity might be ascribed to its high Mw and rich monosaccharide composition.This study offers a solid scientific foundation for the development of AKP for wide clinical application. 展开更多
关键词 structural char Immunological function Neutral polysaccharide Structural characterization areca nut kernels separation purificationsemxrdftirand areca nut kernel polysaccharides akp ultrasonic assisted Areca catechu kernels
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Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium 认领 引用 被引量：4
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作者 Quoc-Hoa Pham Van Ke Tran Phu-Cuong Nguyen 《Defence Technology（防务技术）》 SCIE EI CAS CSCD 2024年第5期77-99,共23页
An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties ... An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums. 展开更多
关键词 Plate-fluid contact Galerkin Vlasov's method Multi-directional functionally graded plate Novel porosity Thermal vibration Refined higher-order shear deformation theory
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Three-dimensional free vibration analysis of multi-directional functionally graded piezoelectric annular plates on elastic foundations via state space based differential quadrature method 认领 引用 被引量：4
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作者 M.H.YAS N.MOLOUDI 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第4期439-464,共26页
The three-dimensional free vibration analysis of a multi-directional func- tionally graded piezoelectric （FGP） annular plate resting on two parameter （Pasternak） elastic foundations is investigated under different... The three-dimensional free vibration analysis of a multi-directional func- tionally graded piezoelectric （FGP） annular plate resting on two parameter （Pasternak） elastic foundations is investigated under different boundary conditions. The material properties are assumed to vary continuously along the radial and thickness directions and have exponent-law distribution. A semi-analytical approach named the state space based differential quadrature method （SSDQM） is used to provide an analytical solution along the thickness using the state space method （SSM） and an approximate solution along the radial direction using the one-dimensional differential quadrature method （DQM）. The influence of the Winkler and shear stiffness of the foundation~ the material property graded variations, and the circumferential wave number on the nomdimensional natural frequency of multi-directional FGP annular plates is studied. 展开更多
关键词 multi-directional functionally graded piezoelectric annular plate freevibration
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Numerical simulation of the fluid and flexible rods interaction using a semi-resolved coupling model promoted by anisotropic Gaussian kernel function 认领 引用
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作者 Caiping Jin Jingxin Zhang Yonglin Sun 《Theoretical & Applied Mechanics Letters》 EI CAS CSCD 2025年第1期5-8,共4页
The numerical simulation of the fluid flow and the flexible rod(s)interaction is more complicated and has lower efficiency due to the high computational cost.In this paper,a semi-resolved model coupling the computatio... The numerical simulation of the fluid flow and the flexible rod(s)interaction is more complicated and has lower efficiency due to the high computational cost.In this paper,a semi-resolved model coupling the computational fluid dynamics and the flexible rod dynamics is proposed using a two-way domain expansion method.The gov-erning equations of the flexible rod dynamics are discretized and solved by the finite element method,and the fluid flow is simulated by the finite volume method.The interaction between fluids and solid rods is modeled by introducing body force terms into the momentum equations.Referred to the traditional semi-resolved numerical model,an anisotropic Gaussian kernel function method is proposed to specify the interactive forces between flu-ids and solid bodies for non-circle rod cross-sections.A benchmark of the flow passing around a single flexible plate with a rectangular cross-section is used to validate the algorithm.Focused on the engineering applications,a test case of a finite patch of cylinders is implemented to validate the accuracy and efficiency of the coupled model. 展开更多
关键词 Semi-resolved coupling model Two-way domain expansion method Anisotropic Gaussian kernel function Flexible rod(s)
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SVM with Quadratic Polynomial Kernel Function Based Nonlinear Model One-step-ahead Predictive Control 认领 引用 被引量：17
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作者 钟伟民 何国龙 +1 位作者 皮道映 孙优贤 《Chinese Journal of Chemical Engineering》 SCIE EI CAS 2005年第3期373-379,共7页
A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identifica... A support vector machine (SVM) with quadratic polynomial kernel function based nonlinear model one-step-ahead predictive controller is presented. The SVM based predictive model is established with black-box identification method. By solving a cubic equation in the feature space, an explicit predictive control law is obtained through the predictive control mechanism. The effect of controller is demonstrated on a recognized benchmark problem and on the control of continuous-stirred tank reactor (CSTR). Simulation results show that SVM with quadratic polynomial kernel function based predictive controller can be well applied to nonlinear systems, with good performance in following reference trajectory as well as in disturbance-rejection. 展开更多
关键词 nonlinear model predictive control support vector machine nonlinear system identification kernel function
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Landslide prediction based on improved principal component analysis and mixed kernel function least squares support vector regression model 认领 引用 被引量：8
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作者 LI Li-min CHENG Shao-kang WEN Zong-zhou 《Journal of Mountain Science》 SCIE CSCD 2021年第8期2130-2142,共13页
Landslide probability prediction plays an important role in understanding landslide information in advance and taking preventive measures.Many factors can influence the occurrence of landslides,which is easy to have a... Landslide probability prediction plays an important role in understanding landslide information in advance and taking preventive measures.Many factors can influence the occurrence of landslides,which is easy to have a curse of dimensionality and thus lead to reduce prediction accuracy.Then the generalization ability of the model will also decline sharply when there are only small samples.To reduce the dimension of calculation and balance the model’s generalization and learning ability,this study proposed a landslide prediction method based on improved principal component analysis(PCA)and mixed kernel function least squares support vector regression(LSSVR)model.First,the traditional PCA was introduced with the idea of linear discrimination,and the dimensions of initial influencing factors were reduced from 8 to 3.The improved PCA can not only weight variables but also extract the original feature.Furthermore,combined with global and local kernel function,the mixed kernel function LSSVR model was framed to improve the generalization ability.Whale optimization algorithm(WOA)was used to optimize the parameters.Moreover,Root Mean Square Error(RMSE),the sum of squared errors(SSE),Mean Absolute Error(MAE),Mean Absolute Precentage Error(MAPE),and reliability were employed to verify the performance of the model.Compared with radial basis function(RBF)LSSVR model,Elman neural network model,and fuzzy decision model,the proposed method has a smaller deviation.Finally,the landslide warning level obtained from the landslide probability can also provide references for relevant decision-making departments in emergency response. 展开更多
关键词 Landslide probability LSSVR Mixed kernel function Improved PCA Warning level
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Multilinear commutators of BMO functions and multilinear singular integrals with non-smooth kernels 认领 引用 被引量：8
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作者 LIAN Jia-li LI Ji WU Huo-xiong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第1期109-120,共12页
This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequaliti... This paper is concerned with certain multilinear commutators of BMO functions and multilinear singular integral operators with non-smooth kernels. By the sharp maximal functions estimates, the weighted norm inequalities for this kind of commutators are established. 展开更多
关键词 Multilineav operator commutator non-smooth kernel sharp maximal function weighted norminequality.
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Commutators of Weighted Lipschitz Functions and Multilinear Singular Integrals with Non-Smooth Kernels 认领 引用 被引量：3
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作者 LIAN Jia-li MA Bo-lin WU Huo-xiong 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第3期353-367,共15页
This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators o... This paper is devoted to studying the commutators of the multilinear singular integral operators with the non-smooth kernels and the weighted Lipschitz functions. Some mapping properties for two types of commutators on the weighted Lebesgue spaces, which extend and generalize some previous results, are obtained. 展开更多
关键词 Commutator multilinear singular integral non-smooth kernel weighted Lipschitz function weights.
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An algorithm for moving target detection in IR image based on grayscale distribution and kernel function 认领 引用 被引量：7
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作者 王鲁平 张路平 +1 位作者 赵明 李飚 《Journal of Central South University》 SCIE EI CAS 2014年第11期4270-4278,共9页
A fast algorithm based on the grayscale distribution of infrared target and the weighted kernel function was proposed for the moving target detection(MTD) in dynamic scene of image series. This algorithm is used to de... A fast algorithm based on the grayscale distribution of infrared target and the weighted kernel function was proposed for the moving target detection(MTD) in dynamic scene of image series. This algorithm is used to deal with issues like the large computational complexity, the fluctuation of grayscale, and the noise in infrared images. Four characteristic points were selected by analyzing the grayscale distribution in infrared image, of which the series was quickly matched with an affine transformation model. The image was then divided into 32×32 squares and the gray-weighted kernel(GWK) for each square was calculated. At last, the MTD was carried out according to the variation of the four GWKs. The results indicate that the MTD can be achieved in real time using the algorithm with the fluctuations of grayscale and noise can be effectively suppressed. The detection probability is greater than 90% with the false alarm rate lower than 5% when the calculation time is less than 40 ms. 展开更多
关键词 moving target detection gray-weighted kernel function dynamic background
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A Full-Newton Step Feasible IPM for Semidefinite Optimization Based on a Kernel Function with Linear Growth Term 认领 引用 被引量：2
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作者 GENG Jie ZHANG Mingwang PANG Jinjuan 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2020年第6期501-509,共9页
In this paper,we propose and analyze a full-Newton step feasible interior-point algorithm for semidefinite optimization based on a kernel function with linear growth term.The kernel function is used both for determini... In this paper,we propose and analyze a full-Newton step feasible interior-point algorithm for semidefinite optimization based on a kernel function with linear growth term.The kernel function is used both for determining the search directions and for measuring the distance between the given iterate and theμ-center for the algorithm.By developing a new norm-based proximity measure and some technical results,we derive the iteration bound that coincides with the currently best known iteration bound for the algorithm with small-update method.In our knowledge,this result is the first instance of full-Newton step feasible interior-point method for SDO which involving the kernel function. 展开更多
关键词 semidefinite optimization interior-point algorithm kernel function iteration complexity
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A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA 认领 引用 被引量：2
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作者 周勇 吴国富 李道纪 《Acta Mathematica Scientia》 SCIE 2006年第4期585-594,共10页
A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations o... A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent. 展开更多
关键词 Truncated data Product-limits quantile function kernel estimator Bahadur representation
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A Full-Newton Step Feasible Interior-Point Algorithm for the Special Weighted Linear Complementarity Problems Based on a Kernel Function 认领 引用 被引量：2
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作者 GENG Jie ZHANG Mingwang ZHU Dechun 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2024年第1期29-37,共9页
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear ... In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and analyzed.The algorithm employs a kernel function with a linear growth term to derive the search direction,and by introducing new technical results and selecting suitable parameters,we prove that the iteration bound of the algorithm is as good as best-known polynomial complexity of interior-point methods.Furthermore,numerical results illustrate the efficiency of the proposed method. 展开更多
关键词 interior-point algorithm weighted linear complementarity problem full-Newton step kernel function iteration complexity
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The choosing of reproducing kernel particle shape function with mathematic proof 认领 引用
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作者 夏茂辉 李金 《Chinese Physics B》 CAS 2007年第10期3067-3071,共5页
Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain anal... Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper. 展开更多
关键词 point of interpolation particle reproducing kernel particle shape function
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ASYMPTOTIC NORMALITY OF KERNEL ESTIMATES OF A DENSITY FUNCTION UNDER ASSOCIATION DEPENDENCE 认领 引用
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作者 林正炎 《Acta Mathematica Scientia》 SCIE 2003年第3期345-350,共6页
Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a k... Let {Xn, n≥1} be a strictly stationary sequence of random variables, which are either associated or negatively associated, f(.) be their common density. In this paper, the author shows a central limit theorem for a kernel estimate of f(.) under certain regular conditions. 展开更多
关键词 Associated random variables negatively associated random variables kernel estimate of a density function central limit theorem
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Interior-point algorithm based on general kernel function for monotone linear complementarity problem 认领 引用
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作者 刘勇 白延琴 《Journal of Shanghai University(English Edition)》 2009年第2期95-101,共7页
A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Un... A polynomial interior-point algorithm is presented for monotone linear complementarity problem （MLCP） based on a class of kernel functions with the general barrier term, which are called general kernel functions. Under the mild conditions for the barrier term, the complexity bound of algorithm in terms of such kernel function and its derivatives is obtained. The approach is actually an extension of the existing work which only used the specific kernel functions for the MLCP. 展开更多
关键词 monotone linear complementarity problem （MLCP） interior-point method kernel function polynomial complexity
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Kernel matrix learning with a general regularized risk functional criterion 认领 引用 被引量：4
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作者 Chengqun Wang Jiming Chen +1 位作者 Chonghai Hu Youxian Sun 《Journal of Systems Engineering and Electronics》 SCIE EI 2010年第1期72-80,共9页
Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is... Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method. 展开更多
关键词 kernel method support vector machine kernel matrix learning HKRS geometric distribution regularized risk functional criterion.
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Bayesian optimized support vector regression with a Gaussian kernel for accurate prediction of the state of health of lithium-ion batteries used for electric vehicle applications 认领 引用
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作者 Selvaraj Vedhanayaki Vairavasundaram Indragandhi 《Global Energy Interconnection》 EI CSCD 2025年第5期891-904,共14页
The state of health SoH of lithium ion batteries plays a predominant role in ensuring the safe and reliable operation of electric vehicles.In this,a novel SoH estimation approach using support vector regression with a... The state of health SoH of lithium ion batteries plays a predominant role in ensuring the safe and reliable operation of electric vehicles.In this,a novel SoH estimation approach using support vector regression with a Gaussian kernel optimized using the Bayesian optimization technique(BO-SVR with a Gaussian kernel)was proposed.Unlike,traditional approaches that use the internal resistance,and battery capacity as input parameters,this study utilized the equivalent discharging voltage difference interval and equivalent charging voltage difference interval,as they capture the dynamic voltage characteristics associated with the battery degradation.The model was simulated using MATLAB 2023a.The mean absolute error,R2,root mean squared error,and mean squared error were considered as performance indicators.The simulation results indicated that the proposed BO-SVR with a Gaussian kernel model had superior performance to other kernel SVR and Gaussian Process Regression models,with a reduced RMSE of 0.0082,thus demonstrating its potential to predict the SoH more accurately. 展开更多
关键词 Lithium-ion batteries State of health Machine learning algorithms Bayesian optimization Kernel function
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Interior-Point Algorithm for Linear Optimization Based on a New Kernel Function 认领 引用 被引量：2
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作者 CHEN Donghai ZHANG Mingwang LI Weihua 《Wuhan University Journal of Natural Sciences》 CAS 2012年第1期12-18,共7页
In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barr... In this paper, we design a primal-dual interior-point algorithm for linear optimization. Search directions and proximity function are proposed based on a new kernel function which includes neither growth term nor barrier term. Iteration bounds both for large-and small-update methods are derived, namely, O（nlog（n/c）） and O（√nlog（n/ε））. This new kernel function has simple algebraic expression and the proximity function has not been used before. Analogous to the classical logarithmic kernel function, our complexity analysis is easier than the other pri- mal-dual interior-point methods based on logarithmic barrier functions and recent kernel functions. 展开更多
关键词 linear optimization interior-point algorithms pri- mal-dual methods kernel function polynomial complexity
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