检索结果-内蒙古大学图书馆

New Douglas-Rashford Splitting Algorithms for Generalized dc programming with Applications in Machine Learning

JOURNAL OF SCIENTIFIC COMPUTING 2025年第3期103卷 1-28页

作者： Yao, Yonghong Jolaoso, Lateef O. Shehu, Yekini Yao, Jen-Chih Tiangong Univ Sch Math Sci Tianjin 300387 Peoples R China China Med Univ China Med Univ Hosp Dept Med Res Taichung Taiwan Kyung Hee Univ Ctr Adv Informat Technol Seoul 02447 South Korea Univ Southampton Sch Math Sci Southampton SO17 1BJ England Sefako Makgatho Hlth Sci Univ Dept Math & Appl Math POB 94 ZA-0204 Pretoria South Africa Zhejiang Normal Univ Sch Math Sci Jinhua 321004 Peoples R China China Med Univ Ctr Gen Educ Taichung 40402 Taiwan Acad Romanian Scientists Bucharest Romania

In this work, we propose some new Douglas-Rashford splitting algorithms for solving a class of generalized dc (difference of convex functions) in real Hilbert spaces. The proposed methods leverage the proximal properties of the nonsmooth component and a fasten control parameter which improves the convergence rate of the algorithms. We prove the convergence of these methods to the critical points of nonconvex optimization under reasonable conditions. We evaluate the performance and effectiveness of our methods through experimentation with three practical examples in machine learning. Our findings demonstrated that our methods offer efficiency in problem-solving and outperform state-of-the-art techniques like the dcA (dc Algorithm) and ADMM.

关键词： Douglas-Rachford splitting algorithm dc programming Nonconvex optimization Machine learning

来源：评论

学校读者我要写书评

暂无评论

Formal Synthesis of Neural Barrier Certificates for Dynamical Systems via dc programming

引用

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 2025年

作者： Wang, Yang Chen, Hanlong Lin, Wang Ding, Zuohua Zhejiang Sci-Tech University School of Computer Science and Technology Hangzhou310018 China

Barrier certificate generation is an ingenious and powerful approach for safety verification of cyber-physical systems. This paper suggests a new learning and verification framework that helps to achieve the balance between the representation ability and the verification efficiency for neural barrier certificates. In the learning phase, it learns candidate barrier certificates represented as convex difference neural networks (CDiNNs). Since CDiNNs can be rewritten as Difference of Convex (dc) functions that can express any twice differentiable function, thus have outstanding representation ability and flexibility. In the verification phase, it employs an efficient approach for formally verifying the validity of the neural candidates via dc programming. Due to the convexity-based structure, CDiNNs can significantly facilitate the verification process. We conduct an experimental evaluation over a set of benchmarks, which validates that our method is much more efficient and effective than the state-of-the-art approaches. © 1982-2012 IEEE.

关键词： Barrier certificates dc programming Formal synthesis Safety verification

来源：评论

学校读者我要写书评

暂无评论

dc programming approaches for discrete portfolio optimization under concave transaction costs

引用

OPTIMIZATION LETTERS 2016年第2期10卷 261-282页

作者： Tao Pham Dinh Hoai An Le Thi Viet Nga Pham Niu, Yi-Shuai Univ Normandie Natl Inst Appl Sci Rouen LMI F-76801 St Etienne France Univ Lorraine Lab Theoret & Appl Comp Sci F-57045 Metz France

The paper investigates dc programming and dcA for both modeling discrete portfolio optimization under concave transaction costs as dc programs, and their solution. dc reformulations are established by using penalty techniques in dc programming. A suitable global optimization branch and bound technique is also developed where a dc relaxation technique is used for lower bounding. Numerical simulations are reported that show the efficiency of dcA and the globality of its computed solutions, compared to standard algorithms for nonconvex nonlinear integer programs.

关键词： Portfolio optimization dc programming dcA Branch and bound dc relaxation Concave transaction costs Nonconvex integer program

来源：评论

学校读者我要写书评

暂无评论

dc programming and dcA for parametric-margin ν-support vector machine

引用

APPLIED INTELLIGENCE 2020年第6期50卷 1763-1774页

作者： Bazikar, Fatemeh Ketabchi, Saeed Moosaei, Hossein Univ Guilan Fac Math Sci Dept Appl Math Rasht Iran Univ Bojnord Dept Math Fac Sci Bojnord Iran

As a development of nu-support vector machine (nu-SVM), parametric-margin nu-support vector machine (Par-nu-SVM) can be useful in many cases, especially heteroscedastic noise classification problems. The present article proposes a novel and fast method to solve the primal problem of Par-nu-SVM (named as dc-Par-nu-SVM), while Par-nu-SVM maximizes the parametric-margin by solving a dual quadratic programming problem. In fact, the primal non-convex problem is converted into an unconstrained problem to express the objective function as the difference of convex functions (dc). The dc-Algorithm (dcA) based on generalized Newton's method is proposed to solve the unconstrained problem cited. Numerical experiments performed on several artificial, real-life, UCI and Ndc data sets showed the superiority of the dc-Par-nu-SVM in terms of both accuracy and learning speed.

关键词： Support vector machine Non-convex optimization Generalized Newton's method dc programming dcA

来源：评论

学校读者我要写书评

暂无评论

dc programming and dcA: thirty years of developments

引用

MATHEMATICAL programming 2018年第1期169卷 5-68页

作者： Hoai An Le Thi Tao Pham Dinh Univ Lorraine Lab Theoret & Appl Comp Sci LITA 3 Rue Augustin Fresnel F-57073 Metz Technopole France Natl Inst Appl Sci Rouen Math Lab F-76801 St Etienne Du Rouvray France

The year 2015 marks the 30th birthday of dc (Difference of Convex functions) programming and dcA (dc Algorithms) which constitute the backbone of nonconvex programming and global optimization. In this article we offer a short survey on thirty years of developments of these theoretical and algorithmic tools. The survey is comprised of three parts. In the first part we present a brief history of the field, while in the second we summarize the state-of-the-art results and recent advances. We focus on main theoretical results and dcA solvers for important classes of difficult nonconvex optimization problems, and then give an overview of real-world applications whose solution methods are based on dcA. The third part is devoted to new trends and important open issues, as well as suggestions for future developments.

关键词： dc programming dcA Theory Algorithms Applications

来源：评论

学校读者我要写书评

暂无评论

dc programming for sparse proximal support vector machines

引用

INFORMATION SCIENCES 2021年 547卷 187-201页

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

Proximal support vector machine (PSVM), as a variant of support vector machine (SVM), is to generate a pair of non-parallel hyperplanes for classification. Although PSVM is one of the powerful classification tools, its ability on feature selection is still weak. To overcome this defect, we introduce l(0)-norm regularization in PSVM which enables PSVM to select important features and remove redundant features simultaneously for classification. This PSVM is called as a sparse proximal support vector machine (SPSVM). Due to the presence of l(0)-norm, the resulting optimization problem of SPSVM is neither convex nor smooth and thus, is difficult to solve. In this paper, we introduce a continuous nonconvex function to approximate l(0)-norm, and propose a novel difference of convex functions algorithms (dcA) to solve SPSVM. The main merit of the proposed method is that all subproblems are smooth and admit closed form solutions. The effectiveness of the proposed method is illustrated by theoretical analysis as well as some numerical experiments on both simulation datasets and real world datasets. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Support vector machine Sparse proximal support vector machine dc programming dc Algorithm

来源：评论

学校读者我要写书评

暂无评论

dc programming and dcA for sparse optimal scoring problem

引用

NEUROCOMPUTING 2016年 186卷 170-181页

作者： Hoai An Le Thi Duy Nhat Phan Ton Duc Thang Univ Dept Management Sci & Technol Dev Ho Chi Minh City Vietnam Ton Duc Thang Univ Fac Math Stat Ho Chi Minh City Vietnam Univ Lorraine LITA Lab Theoret & Appl Comp Sci Ile Saulcy F-57045 Metz France

Linear Discriminant Analysis (LDA) is a standard tool for classification and dimension reduction in many applications. However, the problem of high dimension is still a great challenge for the classical LDA. In this paper we consider the supervised pattern classification in the high dimensional setting, in which the number of features is much larger than the number of observations and present a novel approach to the sparse optimal scoring problem using the zero-norm. The difficulty in treating the zero-norm is overcome by using appropriate continuous approximations such that the resulting problems are solved by alternating schemes based on dc (Difference of Convex functions) programming and dcA (dc Algorithms). The experimental results on both simulated and real datasets show the efficiency of the proposed algorithms compared to the five state-of-the-art methods. (C) 2016 Elsevier B.V. All rights reserved.

关键词： Feature selection Linear discriminant analysis Optimal scoring dc programming dcA Alternating scheme

来源：评论

学校读者我要写书评

暂无评论

dc programming and dcA for supply chain and production management: state-of-the-art models and methods

引用

INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2020年第20期58卷 6078-6114页

作者： Thi, Hoai An Le Univ Lorraine Comp Sci & Applicat Dept LGIPM Metz France

It is undoubtedly that mathematical modelling and optimisation play a key role in the supply chain and the production management (SCPM). In this paper, we provide a survey on dc (Difference of Convex function) programming and dcA (dc Algorithm), a state-of-the-art optimisation approach for challenging problems in SCPM. dc programming and dcA constitute the backbone of non-convex programming and global optimisation. Whilst dc programming and dcA were widely and successfully investigated in many areas, it seems that they were not so much popular in the community of SCPM. There is therefore a need to further develop this efficient and scalable approach for SCPM applications, especially for large-scale problems in the context of Big data. For such purpose, this paper aims to present benchmark models and state-of-the-art dcA-based methods for solving challenging problems in SCPM systems. We prove that all the benchmark classes of optimisation models appeared in SCPM systems can be formulated/reformulated as a dc program and show how to solve these classes of problems by dcA-based algorithms. We offer the community of researchers in SCPM efficient algorithms in a unified dc programming framework to tackle various applications such as supply chain design, scheduling, multi-stage production/inventory system, vehicle routing, horizontal ellipsis

关键词： supply chain production management dc programming dcA exact penalty mixed integer dc programming

来源：评论

学校读者我要写书评

暂无评论

dc programming and dcA for sparse Fisher linear discriminant analysis

引用

NEURAL COMPUTING & APPLICATIONS 2017年第9期28卷 2809-2822页

作者： Hoai An Le Thi Duy Nhat Phan Ton Duc Thang Univ Fac Math Stat Dept Management Sci & Technol Dev Ho Chi Minh City Vietnam Univ Lorraine Lab Theoret & Appl Comp Sci F-57045 Metz France

We consider the supervised pattern classification in the high-dimensional setting, in which the number of features is much larger than the number of observations. We present a novel approach to the sparse Fisher linear discriminant problem using the l(0)-norm. The resulting optimization problem is nonconvex, discontinuous and very hard to solve. We overcome the discontinuity by using appropriate approximations to the l(0)-norm such that the resulting problems can be formulated as difference of convex functions (dc) programs to which dc programming and dc Algorithms (dcA) are investigated. The experimental results on both simulated and real datasets demonstrate the efficiency of the proposed algorithms compared to some state-of-the-art methods.

关键词： Classification Feature selection Fisher linear discriminant analysis dc programming dcA

来源：评论

学校读者我要写书评

暂无评论

dc programming for solving a sparse modeling problem of video key frame extraction

引用

DIGITAL SIGNAL PROCESSING 2018年 83卷 214-222页

作者： Tan, Benying Li, Yujie Ding, Shuxue Paik, Incheon Kanemura, Atsunori Univ Aizu Aizu Wakamatsu 9658580 Japan Natl Inst Adv Ind Sci & Technol Tsukuba Ibaraki 3058560 Japan Adv Telecommun Res Inst Int ATR Kyoto 6190288 Japan LeapMind Inc Tokyo 1500044 Japan

Extracting key frames from a video can reduce redundancies in continuous scenes and pithy represent the entire video. This technique copes with the issue of how to efficiently manage a large amount of video data and has many applications such as video indexing, querying, and browsing. Current key frame extraction methods often utilize sparse modeling, which assumes that each video frame can be expressed as a linear combination of a few representative key frames. Although these methods are successful, they are less aware of the fact that videos have spatio-temporal structure and used l(1) norm based sparsity measure. In this paper, we propose a key frame extraction method that considers spatio-temporal information of videos. We employ a sparsity measure that is based on the determinant of the Gram matrix computed from entire video frames. The determinant sparsity measure is computed for the entire matrix, not for single frames, and thus it reflects the spatial or joint sparseness of the entire video. With this measure, the solutions are sparser than conventional sparseness measures but the cost function is non-convex and optimization becomes harder. Then, utilizing the fact that the proposed cost function is the difference of two convex functions, we employ an efficient algorithm based on the difference-of-convex (dc) programming, which often finds the global solution of the non-convex cost function. Experiments show that the proposed algorithm generates high-quality, high-compression key frames, compared with the existing key frame extraction method with the l(1) norm. The determinant sparsity measure was recently proposed and can be utilized for more video processing applications such as video saliency detection. (C) 2018 Elsevier Inc. All rights reserved.

关键词： Sparse representation Key frame Determinant dc programming Convolutional neural network

来源：评论

学校读者我要写书评

暂无评论

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案：

请选择收藏分类：

通借通还

建议与咨询 留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

时间限定

文献类型

馆藏选择

核心期刊

语言

文献类型

帮助

文字说明：

检索规则说明：

检索范例：

分类表

所选分类

限定检索结果

文献类型

馆藏范围

日期分布

学科分类号

主题

机构

作者

语言

请选择保存的检索档案： 新增检索档案 确定 取消

请选择收藏分类： 新增自定义分类 确定 取消

通借通还

建议与咨询留下您的常用邮箱和电话号码，以便我们向您反馈解决方案和替代方法

请选择保存的检索档案：

请选择收藏分类：