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There are 49 papers published in subject: > since this site started. |
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1. Nonlinear Conjugate Gradient Methods for Scalar and Vector Optimization | |||
ZHANG Bo-Ya,CHEN Chun-Rong | |||
Mathematics 27 February 2024 | |||
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Abstract:The nonlinear conjugate gradient methods utilize gradient information to search for the optimal solutions, and speed up the convergence rate by selecting conjugate search directions, which are characterized by fast convergence, low storage requirements, and wide applicability, as a result, it serves as an effective numerical method for solving nonlinear unconstrained optimization problems. In recent years, the nonlinear conjugate gradient methods have also been applied in the field of vector optimization. The focus of this paper is to introduce the research status and convergence results of some modified nonlinear conjugate gradient methods for scalar optimization, as well as the nonlinear conjugate gradient methods for vector optimization. | |||
TO cite this article:ZHANG Bo-Ya,CHEN Chun-Rong. Nonlinear Conjugate Gradient Methods for Scalar and Vector Optimization[OL].[27 February 2024] http://en.paper.edu.cn/en_releasepaper/content/4762269 |
2. An accelerated sequential minimal optimization method for the least squares support vector machine | |||
Liu Siyi,Liu Jianxun | |||
Mathematics 10 March 2023 | |||
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Abstract:Least squares support vector machine(LS-SVM) is an important variant of traditional support vector machine, which is used to solve pattern recognition and prediction. We propose an improved version of the Sequential minimum optimization(SMO) algorithm for training LS-SVM, based on a acclerated grdient method. In this paper we consider adding a new point to capture previous update information. We adopt the idea of Nesterov acceleration method, which gets intermediate points from previous update information and then updates the new iteration point. we show experimentally that the improvement method can significantly reduce the number of iterations, and the training time of LS-SVM can also be reduced in the improvement first-order SMO. | |||
TO cite this article:Liu Siyi,Liu Jianxun. An accelerated sequential minimal optimization method for the least squares support vector machine[OL].[10 March 2023] http://en.paper.edu.cn/en_releasepaper/content/4759470 |
3. A Brief Survey of Nonlinear Conjugate Gradient Methods for Vector Optimization | |||
HE Qing-Rui,CHEN Chun-Rong | |||
Mathematics 22 December 2022 | |||
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Abstract:Conjugate gradient methods are important first-order algorithms, which are characterized by low memory requirements and strong convergence properties. Conjugate gradient methods were first proposed for solving symmetric and positive-definite linear systems, and then developed into a class of major approaches for solving nonlinear unconstrained minimization problems. In recent years, conjugate gradient methods have been also applied to vector optimization problems. In this paper, we mainly introduce the research status and convergence results of nonlinear conjugate gradient methods for vector optimization, and give an instance to illustrate their practicability. | |||
TO cite this article:HE Qing-Rui,CHEN Chun-Rong. A Brief Survey of Nonlinear Conjugate Gradient Methods for Vector Optimization[OL].[22 December 2022] http://en.paper.edu.cn/en_releasepaper/content/4758680 |
4. A Brief Description of The Proximal Point Method in Optimization and Variational Problems | |||
YE Zi-Shi,Chun-Rong | |||
Mathematics 22 January 2022 | |||
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Abstract:The proximal point method is an important approach for solving generalized equations. It is widely used in solving optimization problems and variational inequalities, and plays an important role in real life and production. This article mainly introduces the research status of the proximal point method, the basic framework of this method, important convergence conclusions and the specific forms of the proximal point method applied to several common problems. | |||
TO cite this article:YE Zi-Shi,Chun-Rong. A Brief Description of The Proximal Point Method in Optimization and Variational Problems[OL].[22 January 2022] http://en.paper.edu.cn/en_releasepaper/content/4756142 |
5. Results on Solution Continuity for Unified Set-valued Vector Equilibrium Problems | |||
Ye XiuLian,CHEN Chun-Rong,CHEN Chun-Rong | |||
Mathematics 12 January 2021 | |||
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Abstract:The stability analysis of unified set-valued vector equilibrium problems via improvement sets is discussed in this paper. First, we obtain the linear scalarization characterizations to solutions for unified weak set-valued vector equilibrium problems and to $E$-Benson proper efficient solutions for unified set-valued vector equilibrium problems. Then, by the linear scalarization characterizations, the solution continuity and the $E$-Benson proper efficient solution continuity for parametric unified weak set-valued vector equilibrium problems and parametric unified set-valued vector equilibrium problems are established, respectively. | |||
TO cite this article:Ye XiuLian,CHEN Chun-Rong,CHEN Chun-Rong. Results on Solution Continuity for Unified Set-valued Vector Equilibrium Problems[OL].[12 January 2021] http://en.paper.edu.cn/en_releasepaper/content/4753460 |
6. Optimizes a convex function on a multi-objective efficient set | |||
Wang Ting,Yao Bin | |||
Mathematics 03 December 2020 | |||
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Abstract:The optimization problem of convex function on effective set of multi-objective optimizationhas many useful applications in multi-criteria decision making. In mathematics, problem (P) can be classified as a global optimization problem.This type of problem is more difficult to solve than convex programming problems.In this paper, penalty function method and parameter method for global optimal solution are proposed, and the cases with equality constraint are discussed. | |||
TO cite this article:Wang Ting,Yao Bin. Optimizes a convex function on a multi-objective efficient set[OL].[ 3 December 2020] http://en.paper.edu.cn/en_releasepaper/content/4753148 |
7. Solution Continuity and Gap Functions with Error Bounds for Vector Equilibrium Problems under Improvement Sets via Scalarization | |||
CHEN Juan,CHEN Chunrong | |||
Mathematics 10 January 2020 | |||
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Abstract:In this paper, firstly, we discuss useful linear scalarization characterizations to solutions for unified vector equilibrium problems via improvement sets. Then, using scalarization methods and main assumptions of generalized convexity and monotonicity, the solution continuity for parametric unified vector equilibrium problems, (regularized) gap functions and error bounds, and gap functions via the minimax strategy for unified vector equilibrium problems under improvement sets are investigated, respectively. Our results generalize or improve related ones in the literature. Especially, the results obtained on (regularized) gap functions and error bounds are general and new. | |||
TO cite this article:CHEN Juan,CHEN Chunrong. Solution Continuity and Gap Functions with Error Bounds for Vector Equilibrium Problems under Improvement Sets via Scalarization[OL].[10 January 2020] http://en.paper.edu.cn/en_releasepaper/content/4750369 |
8. Gap functions and error bounds based on constrained vector variational inequalities | |||
YANG Hu, YAO Bin | |||
Mathematics 17 October 2019 | |||
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Abstract:In this paper,by employing the image space analysis to investigate the constrained vector variational inequality.Firstly,By virtue of the oriented distance function,a new nonlinear regular weak separation function is introduced.By mean of the nonlinear regular weak separation function,a gap function for the constrained vector variational inequality is obtained.Then,as an application of gap functions,error bounds for the constrained vector variational inequalities are dervied.Morever,these bounds offer valid estimated distances between a feasible point and the solution set of the constrained vector variational inequalities. | |||
TO cite this article:YANG Hu, YAO Bin. Gap functions and error bounds based on constrained vector variational inequalities[OL].[17 October 2019] http://en.paper.edu.cn/en_releasepaper/content/4749818 |
9. Research on a second-order cone reformulating problem of CDT problem | |||
QU Yanming | |||
Mathematics 12 March 2019 | |||
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Abstract:In this paper, we study a class of CDT problem with two quadratic constraints, one of which is the unit ball constraint and the other is the ellipsoid constraint. Select the appropriate hyperplane through the optimal line segment, without dividing the feasible region. In the case of the second-order cone recombination technique and the SDP relaxation method, the necessary and sufficient conditions for the existence of the dual gap in the second-order cone reformulating problem of the CDT problem are obtained, and the theoretical proof is given which is paved to reduce or even eliminate the dual gap of the CDT problem. | |||
TO cite this article:QU Yanming. Research on a second-order cone reformulating problem of CDT problem[OL].[12 March 2019] http://en.paper.edu.cn/en_releasepaper/content/4747715 |
10. Scalarization and Optimality Conditions for Vector Equilibrium Problems via Improvement Sets in Real Linear Spaces | |||
LIU Jia,CHEN Chun-Rong | |||
Mathematics 19 September 2018 | |||
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Abstract:In this paper, we study vector equilibrium problems with the ordering relations defined via improvementsets in real linear spaces without assuming any topology. We deal with efficient solutions, weak efficient solutions, Benson and Henig proper efficient solutions. The linear scalarization characterizations of these solutions are established, moreover, optimization conditions via Lagrange multiplier rulers for vector equilibrium problems with constraints are also obtained. Our results generalized the corresponding ones in the literature. | |||
TO cite this article:LIU Jia,CHEN Chun-Rong. Scalarization and Optimality Conditions for Vector Equilibrium Problems via Improvement Sets in Real Linear Spaces[OL].[19 September 2018] http://en.paper.edu.cn/en_releasepaper/content/4746010 |
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