In this paper, we deal with a polynomial primal-dual interior-point algorithm for solving convex quadratic programming based on a new parametric kernel function with an exponential barrier term. The proposed kernel fu...
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In this paper, we deal with a polynomial primal-dual interior-point algorithm for solving convex quadratic programming based on a new parametric kernel function with an exponential barrier term. The proposed kernel function is not logarithmic and not self-regular. We analyze a class of large and small-update versions which are based on our new kernel function. The complexity obtained generalizes the result given by Bai et al. This result is the first to reach this goal. Finally, some numerical results are provided to show the efficiency of the proposed algorithm and to compare it with an available method.
Recently, El Ghami(Optim Theory DecisMak Oper Res Appl 31: 331-349, 2013) proposed a primal dual interior point method for P-*(k)-Linear Complementarity Problem (LCP) based on a trigonometric barrier term and obtained...
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Recently, El Ghami(Optim Theory DecisMak Oper Res Appl 31: 331-349, 2013) proposed a primal dual interior point method for P-*(k)-Linear Complementarity Problem (LCP) based on a trigonometric barrier term and obtained the worst case iteration complexity as O((1 + 2k)n(3/4) log n/is an element of for large-update methods. In this paper, we present a large update primal-dual interior point algorithm for P-*(k)-LCP based on a new trigonometric kernel function. By a simple analysis, we show that our algorithm based on the new kernel function enjoys the worst case O((1 + 2k)root nlog n log n/is an element of iteration bound for solving P-*(k)-LCP. This result improves the worst case iteration bound obtained by El Ghami for P-*(k)-LCP based on trigonometric kernel functions significantly.
Analysis of the dynamic response of a complex nonlinear system is always a difficult *** using Volterra functional series to describe a nonlinear system,its response analysis can be similar to using Fourier/Laplace tr...
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Analysis of the dynamic response of a complex nonlinear system is always a difficult *** using Volterra functional series to describe a nonlinear system,its response analysis can be similar to using Fourier/Laplace transform and linear transfer function method to analyse a linear system’s *** this paper,a dynamic response analysis method for nonlinear systems based on Volterra series is ***,the recursive formula of the least square method is established to solve the Volterra kernel function vector,and the corresponding MATLAB programme is ***,the Volterra kernel vector corresponding to the nonlinear response of a structure under seismic excitation is identified,and the accuracy and applicability of using the kernel vector to predict the response of a nonlinear structure are *** results show that the Volterra kernel function identified by the derived recursive formula can accurately describe the nonlinear response characteristics of a structure under an *** a general nonlinear system,the first three order Volterra kernel function can relatively accurately express its nonlinear response *** addition,the obtained Volterra kernel function can be used to accurately predict the nonlinear response of a structure under the similar type of dynamic load.
In this paper,we present a path-following infeasible interior-point method for P∗(κ)horizontal linear complementarity problems(P∗(κ)-HLCPs).The algorithm is based on a simple kernel function for finding the search d...
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In this paper,we present a path-following infeasible interior-point method for P∗(κ)horizontal linear complementarity problems(P∗(κ)-HLCPs).The algorithm is based on a simple kernel function for finding the search directions and defining the neighborhood of the central *** algorithm follows the central path related to some perturbations of the original problem,using the so-called feasibility and centering steps,along with only full such ***,it has the advantage that the calculation of the step sizes at each iteration is *** complexity result shows that the full-Newton step infeasible interior-point algorithm based on the simple kernel function enjoys the best-known iteration complexity for P∗(κ)-HLCPs.
In this paper we present a large-update primal-dual interior-point algorithm for convex quadratic semi-definite optimization problems based on a new parametric kernel *** goal of this paper is to investigate such a ke...
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In this paper we present a large-update primal-dual interior-point algorithm for convex quadratic semi-definite optimization problems based on a new parametric kernel *** goal of this paper is to investigate such a kernel function and show that the algorithm has the best complexity *** complexity bound is shown to be O(√n log n log n/∈).
Clustering is an unsupervised procedure that divides a set of objects into homogeneous groups. Two types of clustering are possible, Hard clustering and Soft clustering/Fuzzy clustering. Hard clustering is not feasibl...
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Clustering is an unsupervised procedure that divides a set of objects into homogeneous groups. Two types of clustering are possible, Hard clustering and Soft clustering/Fuzzy clustering. Hard clustering is not feasible for complex datasets that contain uncertainty and overlapping clusters, whereas fuzzy clustering efficiently handles it. FCM is sensitive to the initial values and challenging to cluster nonlinear data. A new approach is implemented here with the Fuzzy c-Means (FCM) clustering algorithm to improve the performance. The kernel function ensures the linear separability of complex clusters by projecting the feature space into a higher dimension and not subject to the initial values. The kernel-based FCM (KFCM) optimized the clustering. The relevant features are considered for clustering, and it improves the validity of clusters. The irrelevant features blur the clusters and reduce the quality. Silhouette index (SI) and Davies-Bouldin index (DBI) have been used as the evaluation function. The experiments are conducted on two benchmark datasets and one artificial dataset. The result justifies kernel-based FCM, and the superiority of features reduced kernel-based FCM clustering over other traditional fuzzy clustering techniques.
kernel functions play an important role in the design and analysis of primal-dual interior-point algorithms. They are not only used for determining the search directions but also for measuring the distance between the...
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kernel functions play an important role in the design and analysis of primal-dual interior-point algorithms. They are not only used for determining the search directions but also for measuring the distance between the given iterate and the mu-center for the algorithms. In this paper we present a unified kernel function approach to primal-dual interior-point algorithms for convex quadratic semidefinite optimization based on the Nesterov and Todd symmetrization scheme. The iteration bounds for large- and small-update methods obtained are analogous to the linear optimization case. Moreover, this unifies the analysis for linear, convex quadratic and semidefinite optimizations.
In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and *** algorithm employs a kernel function with a linear growth te...
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In this paper,a new full-Newton step primal-dual interior-point algorithm for solving the special weighted linear complementarity problem is designed and *** 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 ***,numerical results illustrate the efficiency of the proposed method.
In this paper, we present a new barrier function for primal-dual interior-point methods in linear optimization. The proposed kernel function has a trigonometric barrier term. It is shown that in the interior-point met...
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In this paper, we present a new barrier function for primal-dual interior-point methods in linear optimization. The proposed kernel function has a trigonometric barrier term. It is shown that in the interior-point methods based on this function for large-update methods, the iteration bound is improved significantly. For small-update interior-point methods, the iteration bound is the best currently known bound for primal-dual interior-point methods. (c) 2011 Elsevier B.V. All rights reserved.
This paper combines kernel function and Locality Preserving Projections (LPP) in a framework to improve the accuracy of clustering model. Specifically, we first use the kernel function to project each feature into hig...
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ISBN:
(纸本)9781728124858
This paper combines kernel function and Locality Preserving Projections (LPP) in a framework to improve the accuracy of clustering model. Specifically, we first use the kernel function to project each feature into high-dimensional kernel space so as to mine the nonlinear relationship of data. At the same time, the l(1)-norm sparse regularization term is used for feature selection. Besides, LPP saves the local structure of data. Finally, the optimal clustering result is obtained by solving the objective function. Experimental results on six benchmark data sets show that our proposed method is superior to the compared methods in term of clustering tasks.
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