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Continuity of Solution Mappings for Parametric Generalized Set-Valued Weak Vector Equilibrium Problems

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Journal of Systems Science & Complexity 2017年第2期30卷 378-391页

作者： PENG Zaiyun ZHAO Yong yang xinmin College of Mathematics and Statistics Chongqing JiaoTong University Department of Mathematics Sichuan University Department of Mathematics Chongqing Normal University

This paper obtains some stability results for parametric generalized set-valued weak vector equilibrium problem. Under new assumptions, which do not contain any information about solution mappings, the authors establish the continuity of the solution mapping to a parametric generalized set-valued weak vector equilibrium problem without monotonicity. These results extend and improve some results in the literature. Some examples are given to illustrate the results.

关键词： Continuity parametric generalized set-valued weak vector equilibrium problems solution mapping stability.

Alleviating limit cycling in training GANs with an optimization technique

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Science China Mathematics 2024年第6期67卷 1287-1316页

作者： Keke Li Liping Tang xinmin yang National Center for Applied Mathematics in Chongqing Chongqing Normal UniversityChongqing401331China School of Mathematical Sciences University of Electronic Science and Technology of ChinaChengdu611731China

In this paper,we undertake further investigation to alleviate the issue of limit cycling behavior in training generative adversarial networks(GANs)through the proposed predictive centripetal acceleration algorithm(PCAA).Specifically,we first derive the upper and lower complexity bounds of PCAA for a general bilinear game,with the last-iterate convergence rate notably improving upon previous ***,we combine PCAA with the adaptive moment estimation algorithm(Adam)to propose PCAA-Adam,for practical training of GANs to enhance their generalization ***,we validate the effectiveness of the proposed algorithm through experiments conducted on bilinear games,multivariate Gaussian distributions,and the CelebA dataset,respectively.

关键词： GANs general bilinear game predictive centripetal acceleration algorithm lower and upper complexity bounds PCAA-Adam

Continuous-time System Identification with Nuclear Norm Minimization and GPMF-based Subspace Method

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IEEE/CAA Journal of Automatica Sinica 2016年第2期3卷 184-191页

作者： Mingxiang Dai Ying He xinmin yang the National Key Laboratory of Transient Physics Nanjing University of Science and Technology

To improve the accuracy and effectiveness of continuous-time (CT) system identification, this paper introduces a novel method that incorporates the nuclear norm minimization (NNM) with the generalized Poisson moment functional (GPMF) based subspace method. The GPMF algorithm provides a simple linear mapping for subspace identification without the timederivatives of the input and output measurements to avoid amplification of measurement noise, and the NNM is a heuristic convex relaxation of the rank minimization. The Hankel matrix with minimized nuclear norm is used to determine the model order and to avoid the over-parameterization in subspace identification method (SIM). Furthermore, the algorithm to solve the NNM problem in CT case is also deduced with alternating direction methods of multipliers (ADMM). Lastly, two numerical examples are presented to evaluate the performance of the proposed method and to show the advantages of the proposed method over the existing methods. © 2014 Chinese Association of Automation.

关键词： Identification (control systems) Matrix algebra Numerical methods Relaxation processes Religious buildings

D-B-PREINVEX TYPE MAPPINGS

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Journal of Systems Science & Complexity 2006年第1期19卷 93-100页

作者： Jianwen PENG xinmin yang Weidong RONG College of Mathematics and Computer Science Chongqing Normal UniversityChongqing 400047 China Department of Mathematics Inner Mongolia University Hohhot 010021 China

In this paper, such new definitions as D-B-preinvexity, strictly D-B-preinvexity and explicitly D-B-preinvexity for vector-valued mappings are firstly introduced. Then, a sufficient condition of D-B-preinvex mappings is shown. And then the relationship between the explicitly D-B-preinvcxity and the strictly D-B-preinvexity is discussed. Finally, some properties of D-B-preinvex type mappings are given.

关键词： D-B-preinvexity explicitly D-B-preinvexity relationship strictly D-B-preinvexity.

ON THE CONVERGENCE OF A NEW HYBRID PROJECTION ALGORITHM

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Journal of Systems Science & Complexity 2006年第3期19卷 423-430页

作者： Qian LIU Changyu WANG xinmin yang Department of Mathematics Inner Mongolia University Hohhot 010021 China. Institute of Operations Research Qufu Normal University Qufu 273165 China. Department of Mathematics Chongqing Normal University Chongqing 400047 China Department of Mathematics Inner Mongolia University Hohhot 010021 China.

For unconstrained optimization, a new hybrid projection algorithm is presented m the paper. This algorithm has some attractive convergence properties. Convergence theory can be obtained under the condition that Δ↓f（x） is uniformly continuous. If Δ↓f（x） is continuously differentiable pseudo-convex, the whole sequence of iterates converges to a solution of the problem without any other assumptions. Furthermore, under appropriate conditions one shows that the sequence of iterates has a cluster-point if and only if Ω＊ ≠ θ. Numerical examples are given at the end of this paper.

关键词： Global convergence hybrid projection unconstrained optimization.

Gradient-based algorithms for multi-objective bi-level optimization

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Science China Mathematics 2024年第6期67卷 1419-1438页

作者： xinmin yang Wei Yao Haian Yin Shangzhi Zeng Jin Zhang National Center for Applied Mathematics in Chongqing Chongqing401331China School of Mathematical Sciences Chongqing Normal UniversityChongqing401331China Department of Mathematics Southern University of Science and TechnologyShenzhen518055China National Center for Applied Mathematics Shenzhen Shenzhen518000China Department of Mathematics and Statistics University of VictoriaVictoriaBCV8W 2Y2Canada

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of ***,its multi-objective and hierarchical bi-level nature makes it notably ***-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement ***,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical *** address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and ***,we demonstrate the theoretical validity by accomplishing the desirable Pareto *** experiments confirm the practical efficiency of the proposed method and verify the theoretical *** accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA *** results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.

关键词： multi-objective bi-level optimization convergence analysis Pareto stationary learning to optimize

Higher-order Mond-Weir converse duality in multiobjective programming involving cones

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Science China Mathematics 2013年第11期56卷 2389-2392页

作者： yang xinmin yang Jin YIP Tsz Leung TEO Kok Lay Department of Mathematics Chongqing Normal University Department of Applied Mathematics The Hong Kong Polytechnic University Department of Logistics and Maritime Studies The Hong Kong Polytechnic University Department of Mathematics and Statistics Curtin UniversityW.A. 6845 Australia

In this work, we established a converse duality theorem for higher-order Mond-Weir type multiob- jective programming involving cones. This fills some gap in recently work of Kim et al. [Kim D S, Kang H S, Lee Y J, et ... 详细信息

关键词： multiobjective programming higher order Mond-Weir dual model converse duality theorem cones

SYMMETRIC DUALITY FOR A CLASS OF MULTIOBJECTIVE FRACTIONAL PROGRAMMING

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Systems Science and Mathematical Sciences 1997年第1期10卷 66-74页

作者： yang xinmin (Department of Mathematics, Chongqing Normal University, Chongqing 630047, China) 重庆师范学院数学系重庆

A pair of symmetric duals for a class of nondifferentiable multiobjective fractional programmings is formulated, and appropriate duality theorems are established.

关键词： Symmetric duality proper efficient solution multiobjective fractional programming generalized invexity nondifferentiable

GENERALIZED SUBCONVEXLIKE FUNCTIONS AND MULTIPLE OBJECTIVE OPTIMIZATION　

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Systems Science and Mathematical Sciences 1995年第3期8卷 254-259页

作者： yang xinmin(Department of Mathematics, Chongqing Normal University, Chongqing 630047,China) Department of Mathematics Chongqing Normal University Chongqing 630047 China

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关键词： Generalized subconvexlike functions multiple objective properly efficient solutions scalar problem.