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Robust truncated L₂-norm twin support vector machine

INTERNATIONAL JOURNAL OF MACHINE LEARNING AND CYBERNETICS 2021年第12期12卷 3415-3436页

作者： Yang, Linxi Li, Guoquan Wu, Zhiyou Wu, Changzhi Chongqing Normal Univ Dept Math Sci Chongqing 401331 Peoples R China Chongqing Ctr Appl Math Chongqing 401331 Peoples R China Guangzhou Univ Sch Management Guangzhou 510006 Peoples R China

This paper proposes a new robust truncated L-2-norm twin support vector machine ((TSVM)-S-2), where the truncated L-2-norm is used to measure the empirical risk to make the classifiers more robust when encountering lots of outliers. Meanwhile, chance constraints are also employed to specify false positive and false negative error rates. (TSVM)-S-2 considers a pair of chance constrained nonconvex nonsmooth problems. To solve these difficult problems, we propose an efficient iterative method for (TSVM)-S-2 based on difference of convex functions (dc) programs and dc algorithms (dcA). Experiments on benchmark data sets and artificial data sets demonstrate the significant virtues of (TSVM)-S-2 in terms of robustness and generalization performance.

关键词： Twin support vector machine Chance constraint dc programming dc algorithm

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Smoothing techniques and difference of convex functions algorithms for image reconstructions

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OPTIMIZATION 2020年第7-8期69卷 1601-1633页

作者： Nguyen Mau Nam Le Thi Hoai An Giles, Daniel Nguyen Thai An Portland State Univ Farlborz Maseeh Dept Math & Stat Portland OR 97207 USA Univ Lorraine Comp Sci & Applicat Dept LGIPM Metz France Santa Barbara City Coll Dept Math Santa Barbara CA USA Univ Elect Sci & Technol China Inst Fundamental & Frontier Sci Chengdu Sichuan Peoples R China

In this paper, we study characterizations of differentiability for real-valued functions based on generalized differentiation. These characterizations provide the mathematical foundation for Nesterov's smoothing techniques in infinite dimensions. As an application, we provide a simple approach to image reconstructions based on Nesterov's smoothing and algorithms for minimizing differences of convex (dc) functions that involve the regularization.

关键词： Generalized differentiation Nesterov's smoothing techniques dc algorithm image reconstruction

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A sub-additive dc approach to the complementarity problem

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COMPUTATIONAL OPTIMIZATION AND APPLICATIONS 2019年第2期73卷 509-534页

作者： Abdallah, L. Haddou, M. Migot, T. Lebanese Univ Tripoli Lebanon Univ Rennes CNRS UMR 6625 INSA RennesIRMAR F-35000 Rennes France Univ Guelph Dept Math & Stat Guelph ON Canada

In this article, we study a merit function based on sub-additive functions for solving the non-linear complementarity problem (NCP). This leads to consider an optimization problem that is equivalent to the NCP. In the case of a concave NCP this optimization problem is a Difference of Convex (dc) program and we can therefore use dc algorithm to locally solve it. We prove that in the case of a concave monotone NCP, it is sufficient to compute a stationary point of the optimization problem to obtain a solution of the complementarity problem. In the case of a general NCP, assuming that a dc decomposition of the complementarity problem is known, we propose a penalization technique to reformulate the optimization problem as a dc program and prove that local minima of this penalized problem are also local minima of the merit problem. Numerical results on linear complementarity problems, absolute value equations and non-linear complementarity problems show that our method is promising.

关键词： Complementarity problem Difference of convex Merit function dc algorithm

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A New Solution Method for a Mean-Risk Mixed Integer Nonlinear Program in Transportation Network Protection 6th

A New Solution Method for a Mean-Risk Mixed Integer Nonlinea...

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6th International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA)

作者： Luong Vuong Le Quang Thuan Nguyen Duc Quynh Tran Hanoi Univ Sci & Technol Hanoi Vietnam Ind Univ Ho Chi Minh City Ho Chi Minh City Vietnam Vietnam Natl Univ Hanoi Int Sch Hanoi Vietnam

ISBN: (纸本)9783030383640;9783030383633

The paper deals with a transportation network protection problem. The aim is to limit losses due to disasters by choosing an optimal retrofiting plan. The mathematical model given by Lu, Gupte, Huang [11] is a mixed integer non linear optimization problem. Existing solution methods are complicated and their computing time is long. Hence, it is necessary to develop efficient solution methods for the considered model. Our approach is based on dc (difference of two convex functions) programming and dc algorithm (dcA). The original model is first reformulated as a dc program by using exact penalty techniques. We then apply dcA to solve the resulting problem. Numerical results on a small network are reported to see the behavior of dcA. It shows that dcA is fast and the proposed approach is promissing.

关键词： dc programming dc algorithm Penalty function Transportation Retrofitting CVaR

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A Novel Approach for Travel Time Optimization in Single-Track Railway Networks 6th

A Novel Approach for Travel Time Optimization in Single-Trac...

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6th International Conference on Computer Science, Applied Mathematics and Applications (ICCSAMA)

作者： Nguyen Quang Thuan Nguyen Duc Anh Vietnam Natl Univ Hanoi Int Sch Hanoi Vietnam Hanoi Univ Sci & Technol Hanoi Vietnam

ISBN: (纸本)9783030383640;9783030383633

Train scheduling plays an important role in the operation of railways systems. This work focuses on a model of scheduling in which one minimizes the total travel time of trains in a single track railways network. The model can be written in the form of a mixed 0-1 linear program which has the worst case exponential complexity to calculate the optimal solution. In this paper, we propose a computationally efficient approach to solve the train scheduling problem. Our approach is based on a so-called Difference of Convex functions algorithm (dcA) to provide good feasible solutions with finite convergence. The algorithm is tested on three different railway network topologies including one topology introduced in [18] and two practical topologies in Northern Vietnam. The numerical results are encouraging and demonstrate the efficiency of the approach.

关键词： Train scheduling Penalty function dc algorithm

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Double regularization methods for robust feature selection and SVM classification via dc programming

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INFORMATION SCIENCES 2018年 429卷 377-389页

作者： Lopez, Julio Maldonado, Sebastian Carrasco, Miguel Univ Diego Portales Fac Ingn & Ciencias Ejercito 441 Santiago Chile Univ Los Andes Fac Ingn & Ciencias Aplicadas Santiago 12455 Chile

In this work, two novel formulations for embedded feature selection are presented. A second-order cone programming approach for Support Vector Machines is extended by adding a second regularizer to encourage feature elimination. The one- and the zero norm penalties are used in combination with the Tikhonov regularization under a robust setting designed to correctly classify instances, up to a predefined error rate, even for the worst data distribution. The use of the zero norm leads to a nonconvex formulation, which is solved by using Difference of Convex (dc) functions, extending dc programming to second-order cones. Experiments on high-dimensional microarray datasets were performed, and the best performance was obtained with our approaches compared with well-known feature selection methods for Support Vector Machines. (C) 2017 Elsevier Inc. All rights reserved.

关键词： Zero norm Support vector machines Second-order cone programming dc algorithm

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Visualizing data as objects by dc (difference of convex) optimization

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MATHEMATICAL PROGRAMMING 2018年第1期169卷 119-140页

作者： Carrizosa, Emilio Guerrero, Vanesa Morales, Dolores Romero Univ Seville IMUS Inst Matemat Seville Spain Copenhagen Business Sch Frederiksberg Denmark

In this paper we address the problem of visualizing in a bounded region a set of individuals, which has attached a dissimilarity measure and a statistical value, as convex objects. This problem, which extends the standard Multidimensional Scaling Analysis, is written as a global optimization problem whose objective is the difference of two convex functions (dc). Suitable dc decompositions allow us to use the Difference of Convex algorithm (dcA) in a very efficient way. Our algorithmic approach is used to visualize two real-world datasets.

关键词： Data visualization dc functions dc algorithm Multidimensional scaling analysis

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Exact recovery low-rank matrix via transformed affine matrix rank minimization

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NEUROCOMPUTING 2018年 319卷 1-12页

作者： Cui, Angang Peng, Jigen Li, Haiyang Xi An Jiao Tong Univ Sch Math & Stat Xian 710049 Shaanxi Peoples R China Guangzhou Univ Sch Math & Informat Sci Guangzhou 510006 Guangdong Peoples R China Xian Polytech Univ Sch Sci Xian 710048 Shaanxi Peoples R China

The goal of affine matrix rank minimization problem is to reconstruct a low-rank or approximately low-rank matrix under linear constraints. In general, this problem is combinatorial and NP-hard. In this paper, a nonconvex fraction function is studied to approximate the rank of a matrix and translate this NP-hard problem into a transformed affine matrix rank minimization problem. The equivalence between these two problems is established, and we proved that the uniqueness of the global minimizer of transformed affine matrix rank minimization problem also solves affine matrix rank minimization problem if some conditions are satisfied. Moreover, we also proved that the optimal solution to the transformed affine matrix rank minimization problem can be approximately obtained by solving its regularization problem for some proper smaller lambda > 0. Lastly, the dc algorithm is utilized to solve the regularization transformed affine matrix rank minimization problem and the numerical experiments on image inpainting problems show that our method performs effectively in recovering low-rank images compared with some state-of-art algorithms. (c) 2018 Elsevier B.V. All rights reserved.

关键词： Affine matrix rank minimization Transformed affine matrix rank minimization Non-convex fraction function Equivalence dc algorithm

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Maximum-Margin Model for Nearest Prototype Classifiers

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JOURNAL OF ADVANCED COMPUTATIONAL INTELLIGENCE AND INTELLIGENT INFORMATICS 2018年第4期22卷 565-577页

作者： Kusunoki, Yoshifumi Wakou, Chiharu Tatsumi, Keiji Osaka Univ Grad Sch Engn 2-1 Yamada Oka Suita Osaka 5650871 Japan

In this paper, we study nearest prototype classifiers, which classify data instances into the classes to which their nearest prototypes belong. We propose a maximum-margin model for nearest prototype classifiers. To provide the margin, we define a class-wise discriminant function for instances by the negatives of distances of their nearest prototypes of the class. Then, we define the margin by the minimum of differences between the discriminant function values of instances with respect to the classes they belong to and the values of the other classes. The optimization problem corresponding to the maximum-margin model is a difference of convex functions (dc) program. It is solved using a dc algorithm, which is a k-means-like algorithm, i.e., the members and positions of prototypes are alternately optimized. Through a numerical study, we analyze the effects of hyperparameters of the maximum-margin model, especially considering the classification performance.

关键词： nearest prototype classifiers maximum-margin model dc algorithm

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Computing B-Stationary Points of Nonsmooth dc Programs

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MATHEMATICS OF OPERATIONS RESEARCH 2017年第1期42卷 95-118页

作者： Pang, Jong-Shi Razaviyayn, Meisam Alvarado, Alberth Univ Southern Calif Dept Ind & Syst Engn Los Angeles CA 90089 USA Univ Galileo Dept Appl Math Guatemala City 01010 Guatemala

Motivated by a class of applied problems arising from physical layer based security in a digital communication system, in particular, by a secrecy sum-rate maximization problem, this paper studies a nonsmooth, difference-of-convex (dc) minimization problem. The contributions of this paper are (i) clarify several kinds of stationary solutions and their relations;(ii) develop and establish the convergence of a novel algorithm for computing a d-stationary solution of a problem with a convex feasible set that is arguably the sharpest kind among the various stationary solutions;(iii) extend the algorithm in several directions including a randomized choice of the subproblems that could help the practical convergence of the algorithm, a distributed penalty approach for problems whose objective functions are sums of dc functions, and problems with a specially structured (nonconvex) dc constraint. For the latter class of problems, a pointwise Slater constraint qualification is introduced that facilitates the verification and computation of a B(ouligand)-stationary point.

关键词： nonsmooth dc programming dc constraints dc algorithm stationary solutions Bouligand derivatives randomization

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