随机广义拟变分不等式的迭代解法及应用

王雁南; 曾嘉钦; 黄南京

doi:10.21656/1000-0887.440199

随机广义拟变分不等式的迭代解法及应用

doi: 10.21656/1000-0887.440199

四川大学数学学院，成都 610064

基金项目:

国家自然科学基金项目 12171339

国家重点研发项目 2020YFC0832404

详细信息

作者简介:
王雁南(1998—)，男，硕士生(E-mail: 1255819341@qq.com)

曾嘉钦(1999—)，男，硕士生(E-mail: 185459413@qq.com)

通讯作者:
黄南京(1962—)，男，教授，博士生导师(通讯作者. E-mail: nanjinghuang@hotmail.com; njhuang@scu.edu.cn)

(我刊编委黄南京来稿)
中图分类号: O177.91;O221.5
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出版历程
- 收稿日期: 2023-06-29
- 修回日期: 2023-07-21
- 刊出日期: 2023-11-01

Iterative Methods for Random Generalized Quasi Variational Inequalities With Applications

School of Mathematics, Sichuan University, Chengdu 610064, P.R.China

(Contributed by HUANG Nanjing, M. AMM Ediorial Board)

摘要

摘要: 为了获得Hilbert空间中一类随机广义拟变分不等式的迭代解法, 证明了点到由具闭(凸)值的随机集值映射所刻画的变约束集上的投影算子的可测性.利用该可测性结果和可测选择定理, 构造了求解随机广义拟变分不等式的随机迭代算法.在单调性及Lipschitz连续性条件下, 获得了由算法生成的随机序列的收敛性.作为应用, 给出了随机广义Nash博弈和随机Walrasian均衡问题的一些刻画性结果.
- 随机拟变分不等式 /
- 随机迭代算法 /
- 收敛性 /
- 随机Nash均衡 /
- 随机Walrasian均衡
Abstract: To obtain the iterative methods for solving a class of random generalized quasi variational inequalities (RGQVIs) in the Hilbert spaces, the measurability of the projection operators on varying-constraint sets depicted by the mapping from points to random-value sets with closed (convex) values, was proved. Moreover, the random iterative algorithm was proposed for solving RGQVIs, and the convergence of the random sequences generated with the random iterative algorithm was obtained under some suitable conditions of monotony and Lipschitz continuity. Finally, 2 applications were given with depicting results of the random generalized Nash games and random Walrasian equilibrium problems, respectively.
- random quasi variational inequality /
- random iterative algorithm /
- convergence /
- random Nash equilibrium /
- random Walrasian equilibrium
(Contributed by HUANG Nanjing, M. AMM Ediorial Board)
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1) (我刊编委黄南京来稿)

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参考文献(32)

[1]	MOSCO U. Implicit variational problems and quasi-variational inequalities[J]. Nonlinear Operators and the Calculus of Variations, 1976, 543: 83-156.
[2]	CHAN D, PANG J S. The generalized quasi-variational inequality problem[J]. Mathematics of Operations Research, 1982, 7(2): 159-318. doi: 10.1287/moor.7.2.159
[3]	BAIOCCHI C, CAPELO A. Variational and Quasivariational Inequalities, Application to Free Boundary Problems[M]. New York: Wiley, 1984.
[4]	HARKERP T. Generalized Nash games and quasi-variational inequalities[J]. European Journal of Operational Research, 1991, 54(1): 81-94. doi: 10.1016/0377-2217(91)90325-P
[5]	GIANNESSI F, MAUGERI A. Variational Inequalities and Network Equilibrium Problems[M]. Boston: Springer, 1995.
[6]	KONNOV I V, VOLOTSKAYA E O. Mixed variational inequalities and economic equilibrium problems[J]. Journal of Applied Mathematics, 2002, 2(6): 289-314. doi: 10.1155/S1110757X02106012
[7]	FACCHINEI F, FISCHER A, PICCIALLI V. On generalized Nash games and variational inequalities[J]. Operations Research Letters, 2007, 35(2): 159-164. doi: 10.1016/j.orl.2006.03.004
[8]	张石生. 变分不等式及其相关问题[M]. 重庆: 重庆出版社, 2008. ZHANG Shisheng. Variational Inequality and Its Related Problems[M]. Chongqing: Chongqing Publishing Group, 2008. (in Chinese)
[9]	GWINNER J, RACITI F. Some equilibrium problems under uncertainty and random variational inequalities[J]. Annals of Operations Research, 2012, 200(1): 299-319. doi: 10.1007/s10479-012-1109-2
[10]	LI X, LI X S, HUANG N J. A generalized f-projection algorithm for inverse mixed variational inequalities[J]. Optimization Letters, 2014, 8: 1063-1076. doi: 10.1007/s11590-013-0635-4
[11]	NAGURNEY A. Network Economics: a Variational Inequality Approach[M]. Springer Dordrecht, 1999.
[12]	PANG J S, FUKUSHIMA M. Quasi-variational inequalities, generalized Nash equilibria, and multi-leader-follower games[J]. Computational Management Science, 2005, 2: 21-56. doi: 10.1007/s10287-004-0010-0
[13]	王霄婷, 龙宪军, 彭再云. 求解非单调变分不等式的一种二次投影算法[J]. 应用数学和力学, 2022, 43(8): 927-934. doi: 10.21656/1000-0887.420414 WANG Xiaoting, LONG Xianjun, PENG Zaiyun. A double projection algorithm for solving non-monotone variational inequalities[J]. Applied Mathematics and Mechanics, 2022, 43(8): 927-934. (in Chinese) doi: 10.21656/1000-0887.420414
[14]	杨军. 非单调变分不等式黄金分割算法研究[J]. 应用数学和力学, 2021, 42(7): 764-770. doi: 10.21656/1000-0887.410359 YANG Jun. A golden ratio algorithm for solving nonmonotone variational inequalities[J]. Applied Mathematics and Mechanics, 2021, 42(7): 764-770. (in Chinese) doi: 10.21656/1000-0887.410359
[15]	刘爽, 莫定勇, 周志昂. Riemann流形上ρ-(η, d)-B不变凸的向量变分不等式及向量优化问题[J]. 应用数学和力学, 2020, 41(4): 458-466. doi: 10.21656/1000-0887.400227 LIU Shuang, MO Dingyong, ZHOU Zhiang. Vector variational-like inequalities and vector optimization problems involving ρ-(η, d)-B invexity on Riemannian manifolds[J]. Applied Mathematics and Mechanics, 2020, 41(4): 458-466. (in Chinese) doi: 10.21656/1000-0887.400227
[16]	王梓坤. 随机泛函分析引论[J]. 数学进展, 1962, 5(1): 45-71. https://www.cnki.com.cn/Article/CJFDTOTAL-SXJZ196201001.htm WANG Zikun. Introduction to random functional analysis[J]. Advances in Mathematics, 1962, 5(1): 45-71. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SXJZ196201001.htm
[17]	张石生, 朱元国. 关于一类随机变分不等式和随机拟变分不等式问题[J]. 数学研究与评论, 1989, 9(3): 385-393. https://www.cnki.com.cn/Article/CJFDTOTAL-SXYJ198903014.htm ZHANG Shisheng, ZHU Yuanguo. On a class of random variational inequalities and random quasi-variational inequalities[J]. Journal of Mathematical Research and Exposition, 1989, 9(3): 385-393. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SXYJ198903014.htm
[18]	TAN N X. Random quasi-variational inequality[J]. Mathematische Nachrichten, 1986, 125: 319-328. doi: 10.1002/mana.19861250124
[19]	黄南京. 随机广义集值拟补问题[D]. 硕士学位论文. 成都: 四川大学, 1990. HUANG Nanjing. Random general set-valued quasi complementarity problems[D]. Mater Thesis. Chengdu: Sichuan University, 1990. (in Chinese)
[20]	黄南京. 随机广义集值强非线性拟变分不等式[J]. 四川大学学报(自然科学版), 1994, 31(4): 420-425. https://www.cnki.com.cn/Article/CJFDTOTAL-SCDX404.001.htm HUANG Nanjing. Random general set-valued strongly nonlinear quasivariational inequalities[J]. Journal of Sichuan University (Natural Science Edition), 1994, 31(4): 420-425. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-SCDX404.001.htm
[21]	HUANG N J, CHO Y J. Random completely generalized set-valued implicit quasi-variational inequalities[J]. Positivity, 1999, 3: 201-213.
[22]	DANIELE P, GIUFFRE· S. Random variational inequalities and the random traffic equilibrium problem[J]. Journal of Optimization Theory and Applications, 2014, 167(1): 363-381.
[23]	GWINNER J, JADAMBA B, KHAN A A, et al. Uncertainty Quantification in Variational Inequalities[M]. New York : Chapman and Hall/CRC, 2022.
[24]	HIMMELBERG C J. Measurable relations[J]. Fundamenta Mathematicae, 1975, 87: 53-72.
[25]	CASTAING C, VALADIER M. Convex Analysis and Measurable Multifunctions[M]. Berlin: Springer, 1977.
[26]	张文修, 李寿梅, 汪振鹏, 等. 集值随机过程引论[M]. 北京: 科学出版社, 2007. ZHANG Wenxiu, LI Shoumei, WANG Zhenpeng, et al. Introduction to Set-Valued Random Processes[M]. Beijing: Science Press, 2007. (in Chinese)
[27]	周叔子. 椭圆变分不等式的扰动[J]. 中国科学(A辑), 1991, 21(3): 237-244. https://www.cnki.com.cn/Article/CJFDTOTAL-JAXK199103001.htm ZHOU Shuzi. Perturbation of elliptic variational inequalities[J]. Science China A, 1991, 21(3): 237-244. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JAXK199103001.htm
[28]	张讲社, 徐宗本. 拟变分不等式的迭代解法[J]. 工程数学学报, 1989, 6(1): 40-43. https://www.cnki.com.cn/Article/CJFDTOTAL-GCSX198901005.htm ZHANG Jiangshe, XU Zongben. Iterative methods for quasivariational inequalities[J]. Journal of Engineering Mathematics, 1989, 6(1): 40-43. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-GCSX198901005.htm
[29]	GÓRNIEWICZ L. Topological Fixed Point Theory of Multivalued Mappings[M]. Springer Dordrecht, 1999.
[30]	HE X L. On ϕ-strongly accretive mappings and some set-valued variational problems[J]. Journal of Mathematical Analysis and Applications, 2003, 277(2): 504-511.
[31]	ZHANG Y J, GOU Z, HUANG N J, et al. A class of stochastic differential variational inequalities with some applications[J]. Journal of Nonlinear and Convex Analysis, 2023, 24: 75-100.
[32]	ZHANG Y J, CHEN T, HUANG N J, et al. Penalty method for solving a class of stochastic differential variational inequalities with an application[J]. Nonlinear Analysis: Real World Applications, 2023, 73: 103889.

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随机广义拟变分不等式的迭代解法及应用

doi: 10.21656/1000-0887.440199

作者简介:
王雁南(1998—)，男，硕士生(E-mail: 1255819341@qq.com)

曾嘉钦(1999—)，男，硕士生(E-mail: 185459413@qq.com)

通讯作者:
黄南京(1962—)，男，教授，博士生导师(通讯作者. E-mail: nanjinghuang@hotmail.com; njhuang@scu.edu.cn)

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Iterative Methods for Random Generalized Quasi Variational Inequalities With Applications

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目录

留言板

随机广义拟变分不等式的迭代解法及应用

doi: 10.21656/1000-0887.440199

作者简介: 王雁南(1998—)，男，硕士生(E-mail: 1255819341@qq.com) 曾嘉钦(1999—)，男，硕士生(E-mail: 185459413@qq.com)

通讯作者: 黄南京(1962—)，男，教授，博士生导师(通讯作者. E-mail: nanjinghuang@hotmail.com; njhuang@scu.edu.cn)

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出版历程

Iterative Methods for Random Generalized Quasi Variational Inequalities With Applications

计量

出版历程

目录

作者简介:
王雁南(1998—)，男，硕士生(E-mail: 1255819341@qq.com)

曾嘉钦(1999—)，男，硕士生(E-mail: 185459413@qq.com)

通讯作者:
黄南京(1962—)，男，教授，博士生导师(通讯作者. E-mail: nanjinghuang@hotmail.com; njhuang@scu.edu.cn)