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SUPPORT VECTOR MACHINE BASED ON RANDOM SET SAMPLES

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS 2013年第sup1期21卷 101-112页

作者： Wang, Chao Ha, Minghu Chen, Jiqiang Xing, Hongjie Hebei Univ Coll Phys Sci & Technol Baoding Peoples R China Hebei Univ Engn Sch Econ & Management Handan Peoples R China Hebei Univ Engn Sch Sci Handan Peoples R China Hebei Univ Coll Math & Comp Sci Baoding Peoples R China

In order to deal with learning problems of random set samples encountered in real-world, according to random set theory and convex quadratic programming, a new support vector machine based on random set samples is con... 详细信息

关键词： Random set convex quadratic programming structural risk minimization principle support vector machine

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The cyclic Barzilai-Borwein method for unconstrained optimization

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IMA JOURNAL OF NUMERICAL ANALYSIS 2006年第3期26卷 604-627页

作者： Dai, Yu-Hong Hager, William W. Schittkowski, Klaus Zhang, Hongchao Chinese Acad Sci Acad Math & Syst Sci Inst Math & Sci Engn Comp State Key Lab Sci & Engn Comp Beijing 100084 Peoples R China Univ Florida Dept Math Gainesville FL 32611 USA Univ Bayreuth Dept Comp Sci D-95440 Bayreuth Germany

In the cyclic Barzilai-Borwein (CBB) method, the same Barzilai-Borwein (BB) stepsize is reused for m consecutive iterations. It is proved that CBB is locally linearly convergent at a local minimizer with positive definite Hessian. Numerical evidence indicates that when m > n/2 >= 3, where n is the problem dimension, CBB is locally superlinearly convergent. In the special case m = 3 and n = 2, it is proved that the convergence rate is no better than linear, in general. An implementation of the CBB method, called adaptive cyclic Barzilai-Borwein (ACBB), combines a non-monotone line search and an adaptive choice for the cycle length m. In numerical experiments using the CUTEr test problem library, ACBB performs better than the existing BB gradient algorithm, while it is competitive with the well-known PRP+ conjugate gradient algorithm.

关键词： unconstrained optimization gradient method convex quadratic programming non-monotone line search

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Content- and disparity-adaptive stereoscopic image retargeting

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JOURNAL OF MODERN OPTICS 2016年第3期63卷 207-218页

作者： Yan, Weiqing Hou, Chunping Zhou, Yuan Xiang, Wei Tianjin Univ Sch Elect Informat Engn Tianjin 300072 Peoples R China Univ So Queensland Sch Mech & Elect Engn Toowoomba Qld 4350 Australia

The paper proposes a content- and disparity-adaptive stereoscopic image retargeting. To simultaneously avoid the saliency content and disparity distortion, firstly, we calculate the image saliency region distortion difference, and conclude the factors causing visual distortion. Then, the proposed method via a convex quadratic programming can simultaneously avoid the distortion of the salient region and adjust disparity to a target area, by considering the relationship of the scaling factor of salient region and the disparity scaling factor. The experimental results show that the proposed method is able to successfully adapt the image disparity to the target display screen, while the salient objects remain undistorted in the retargeted stereoscopic image.

关键词： stereoscopic display stereoscopic image disparity adjustment content-aware retargeting convex quadratic programming

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On a primal-dual Newton proximal method for convex quadratic programs

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2022年第2期81卷 369-395页

作者： De Marchi, Alberto Univ Bundeswehr Munchen D-85577 Neubiberg Munich Germany

This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method. The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. This allows the inner Newton scheme to exploit sparse symmetric linear solvers and multi-rank factorization updates. Moreover, the linear systems are always solvable independently from the problem data and exact linesearch can be performed. The proposed method can handle degenerate problems, provides a mechanism for infeasibility detection, and can exploit warm starting, while requiring only convexity. We present details of our open-source C implementation and report on numerical results against state-of-the-art solvers. QPDO proves to be a simple, robust, and efficient numerical method for convex quadratic programming.

关键词： Semismooth Newton method Proximal point method Regularized primal-dual method convex quadratic programming

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convex ensemble learning with sparsity and diversity

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INFORMATION FUSION 2014年第1期20卷 49-59页

作者： Yin, Xu-Cheng Huang, Kaizhu Yang, Chun Hao, Hong-Wei Univ Sci & Technol Beijing Sch Comp & Commun Engn Dept Comp Sci & Technol Beijing 100083 Peoples R China Univ Sci & Technol Beijing Sch Comp & Commun Engn Beijing Key Lab Mat Sci Knowledge Engn Beijing 100083 Peoples R China Xian Jiaotong Liverpool Univ Dept Elect & Elect Engn Suzhou 215123 Peoples R China Chinese Acad Sci Inst Automat Beijing 100190 Peoples R China

Classifier ensemble has been broadly studied in two prevalent directions, i.e., to diversely generate classifier components, and to sparsely combine multiple classifiers. While most current approaches are emphasized on either sparsity or diversity only, we investigate classifier ensemble focused on both in this paper. We formulate the classifier ensemble problem with the sparsity and diversity learning in a general mathematical framework, which proves beneficial for grouping classifiers. In particular, derived from the error-ambiguity decomposition, we design a convex ensemble diversity measure. Consequently, accuracy loss, sparseness regularization, and diversity measure can be balanced and combined in a convex quadratic programming problem. We prove that the final convex optimization leads to a closed-form solution, making it very appealing for real ensemble learning problems. We compare our proposed novel method with other conventional ensemble methods such as Bagging, least squares combination, sparsity learning, and AdaBoost, extensively on a variety of UCI benchmark data sets and the Pascal Large Scale Learning Challenge 2008 webspam data. Experimental results confirm that our approach has very promising performance. (C) 2013 Elsevier B.V. All rights reserved.

关键词： Classifier ensemble Sparsity Diversity convex quadratic programming

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A new variable reduction technique for convex integer quadratic programs

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APPLIED MATHEMATICAL MODELLING 2008年第2期32卷 224-231页

作者： Hua, Zhongsheng Zhang, Bin Xu, Xiaoyan Univ Sci & Technol China Sch Management Anhua 230026 Peoples R China

convex integer quadratic programming involves minimization of a convex quadratic objective function with affine constraints and is a well-known NP-hard problem with a wide range of applications. We proposed a new variable reduction technique for convex integer quadratic programs (IQP). Based on the optimal values to the continuous relaxation of IQP and a feasible solution to IQP, the proposed technique can be applied to fix some decision variables of an IQP simultaneously at zero without sacrificing optimality. Using this technique, computational effort needed to solve IQP can be greatly reduced. Since a general convex bounded IQP (BIQP) can be transformed to a convex IQP, the proposed technique is also applicable for the convex BIQP. We report a computational study to demonstrate the efficacy of the proposed technique in solving quadratic knapsack problems. (c) 2006 Elsevier Inc. All rights reserved.

关键词： integer quadratic programming variable reduction convex quadratic programming quadratic knapsack problem

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Multi-View Support Vector Machines with the Consensus and Complementarity Information

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IEEE TRANSACTIONS ON KNOWLEDGE AND DATA ENGINEERING 2020年第12期32卷 2401-2413页

作者： Xie, Xijiong Sun, Shiliang Ningbo Univ Sch Informat Sci & Engn Ningbo 315211 Peoples R China East China Normal Univ Dept Comp Sci & Technol 3363 North ZhongShan Rd Shanghai 200062 Peoples R China

Multi-view learning (MVL) is an active direction in machine learning that aims at exploiting the consensus and complementarity information among multiple distinct feature sets to boost the generalization performance of the counterpart algorithm. So far, two classical SVM-based MVL methods are SVM-2K and multi-view twin support vector machine (MvTSVM). They are designed only for two-view classification and cannot tackle the general multi-view classification problem. They also cannot effectively leverage the complementarity information among different feature views. In this paper, we propose two novel multi-view support vector machines with the consensus and complementarity information for MVL that not only can deal with the two-view classification problem but also the general multi-view classification problem by jointly learning multiple different views in a non-pairwise way. The disagreement among different views is regarded as a constraint or a regularization term in the objective function which plays an important role in exploring the consensus information. Combination weights for the reconstruction of each view in regularization terms are learned to explore complementarity information among different views. Finally, an efficient iteration algorithm with the classical convex quadratic programming is developed for optimization. Experimental results validate the effectiveness of our proposed methods.

关键词： Multi-view learning SVM-2K multi-view twin support vector machine convex quadratic programming

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IMPLEMENTING PROXIMAL POINT METHODS FOR LINEAR-programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1990年第3期65卷 531-554页

作者： WRIGHT, SJ 1. Department of Mathematics North Carolina State University Raleigh North Carolina

We describe the application of proximal point methods to the linear programming problem. Two basic methods are discussed. The first, which has been investigated by Mangasarian and others, is essentially the well-known method of multipliers. This approach gives rise at each iteration to a weakly convex quadratic program which may be solved inexactly using a point-SOR technique. The second approach is based on the proximal method of multipliers, originally proposed by Rockafellar, for which the quadratic program at each iteration is strongly convex. A number of techniques are used to solve this subproblem, the most promising of which appears to be a two-metric gradient-projection approach. Convergence results are given, and some numerical experience is reported.

关键词： Linear programming method of multipliers convex quadratic programming

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UPDATING CONSTRAINT PRECONDITIONERS FOR KKT SYSTEMS IN quadratic programming VIA LOW-RANK CORRECTIONS

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SIAM JOURNAL ON OPTIMIZATION 2015年第3期25卷 1787-1808页

作者： Bellavia, Stefania De Simone, Valentina di Serafino, Daniela Morini, Benedetta Univ Firenze Dipartimento Ingn Ind I-50134 Florence Italy Univ Naples 2 Dipartimento Matemat & Fis I-81100 Caserta Italy CNR Ist Calcolo & Reti Ad Alte Prestaz I-80131 Naples Italy

This work focuses on the iterative solution of sequences of KKT linear systems arising in interior point methods applied to large convex quadratic programming problems. This task is the computational core of the interior point procedure, and an efficient preconditioning strategy is crucial for the efficiency of the overall method. Constraint preconditioners are very effective in this context;nevertheless, their computation may be very expensive for large-scale problems, and resorting to approximations of them may be convenient. Here we propose a procedure for building inexact constraint preconditioners by updating a seed constraint preconditioner computed for a KKT matrix at a previous interior point iteration. These updates are obtained through low-rank corrections of the Schur complement of the (1,1) block of the seed preconditioner. The updated preconditioners are analyzed both theoretically and computationally. The results obtained show that our updating procedure, coupled with an adaptive strategy for determining whether to reinitialize or update the preconditioner, can enhance the performance of interior point methods on large problems.

关键词： KKT systems constraint preconditioners matrix updates convex quadratic programming interior point methods

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Suboptimal explicit receding horizon control via approximate multiparametric quadratic programming

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 2003年第1期117卷 9-38页

作者： Bemporad, A Filippi, C Univ Siena Dipartimento Ingn Informaz I-53100 Siena Italy Univ Padua Dipartimento Matemat Pura & Applicata I-35131 Padua Italy

Algorithms for solving multiparametric quadratic programming (MPQP) were recently proposed in Refs. 1-2 for computing explicit receding horizon control (RHC) laws for linear systems subject to linear constraints on input and state variables. The reason for this interest is that the solution to MPQP is a piecewise affine function of the state vector and thus it is easily implementable online. The main drawback of solving MPQP exactly is that, whenever the number of linear constraints involved in the optimization problem increases, the number of polyhedral cells in the piecewise affine partition of the parameter space may increase exponentially. In this paper, we address the problem of finding approximate solutions to MPQP, where the degree of approximation is arbitrary and allows to tradeoff between optimality and a smaller number of cells in the piecewise affine solution. We provide analytic formulas for bounding the errors on the optimal value and the optimizer, and for guaranteeing that the resulting suboptimal RHC law provides closed-loop stability and constraint fulfillment.

关键词： receding horizon control model predictive control multiparametric programming convex quadratic programming error bounds piecewise linear control

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