求解伪单调变分不等式问题的惯性收缩投影算法

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O224

Yuehong He,Xianjun Long. A Inertial Contraction and Projection Algorithm for Pseudomonotone Variational Inequality Problems[J].Acta mathematica scientia,Series A, 2021, 41(6): 1897-1911.

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1	Facchinei F, Pang J S. Finite-Dimensional Variational Inequalities and Complementarity Problems. New York: Springer, 2003
2	Goebel K, Reich S. Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings. New York: Marcel Dekker, 1983
3	He B . A class of projection and contraction methods for monotone variational inequalities. Appl Math Optim, 1997, 35 (1): 69- 76 doi: 10.1007/s002459900037
4	Cai X , Gu G , He B . On the O(1/t) convergence rate of the projection and contraction methods for variational inequalities with Lipschitz continuous monotone operators. Comput Optim Appl, 2014, 57 (2): 339- 363 doi: 10.1007/s10589-013-9599-7
5	Censor Y , Gibali A , Reich S . The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl, 2011, 148 (2): 318- 335 doi: 10.1007/s10957-010-9757-3
6	万升联. 解变分不等式的一种二次投影算法. 数学物理学报, 2021, 41A(1): 237-244
	Wan S L. A double projection algorithm for solving variational inequalities. 2021, 41A(1): 237-244
7	Tseng P . A modified forward-backward splitting method for maximal monotone mappings. SIAM J Control Optim, 2000, 38 (2): 431- 446 doi: 10.1137/S0363012998338806
8	Karamardian S . Complementarity problems over cones with monotone and pseudo-monotone maps. J Optim Theory Appl, 1976, 18 (4): 445- 454 doi: 10.1007/BF00932654
9	Korpelevich G M . The extragradient method for finding saddle points and other problems. Ekonomika i Mat Metody, 1976, 12, 747- 756
10	Dong L Q , Cho Y J , Zhong L L , Rassias M T . Inertial projection and contraction algorithms for variational inequalities. J Glob Optim, 2018, 70 (3): 687- 704 doi: 10.1007/s10898-017-0506-0
11	Thong D V , Vinh N T , Cho Y J . New strong convergence theorem of the inertial projection and contraction method for variational inequality problems. Numer Algor, 2020, 84 (1): 285- 305 doi: 10.1007/s11075-019-00755-1
12	Yang J , Liu H W . Strong convergence result for solving monotone variational inequalities in Hilbert space. Numer Algor, 2019, 80 (3): 741- 752 doi: 10.1007/s11075-018-0504-4
13	Gibali A , Thong D V , Tuan P A . Two simple projection-type methods for solving variational inequalities. Anal Math Phys, 2019, 9, 2203- 2225 doi: 10.1007/s13324-019-00330-w
14	Maingé P E . A hybrid extragradient-viscosity method for monotone operators and fixed point problems. SIAM J Control Optim, 2008, 47 (3): 1499- 1515 doi: 10.1137/060675319
15	Xu H K . Iterative algorithms for nonlinear operators. J Lond Math Soc, 2002, 66 (1): 240- 256 doi: 10.1112/S0024610702003332

	$u_0 = {(t^3+1)e^{-t}}$		$u_0 = \frac{1}{500}[{\rm cost}+\sin(-5t)]$		$u_0 = \frac{1}{600}(t^2-e^{-t})$
	Iter	Time	Iter	Time	Iter	Time
NIPCM	6	0.0429	8	0.0535	7	0.0427
VPTA	33	0.0238	125	0.1098	78	0.0573
Y.L	340	0.0437	340	0.0319	340	0.0525
IPCM	533	0.0567	533	0.0612	533	0.0633

	$\epsilon = 10^{-4}$		$\epsilon = 10^{-10}$		$\epsilon = 10^{-20}$		$\epsilon = 10^{-30}$
	Iter	Time	Iter	Time	Iter	Time	Iter	Time
NIPCM	32	0.7108	61	1.1787	79	1.4880	88	2.1495
VTPA	40	9.0375	40	10.3125	40	10.8281	40	9.8906
Y.L	64	3.2096	66	2.4719	69	3.3800	68	2.9023
IPCM	-	$>50$	-	$>50$	-	$>50$	-	$>50$

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A Inertial Contraction and Projection Algorithm for Pseudomonotone Variational Inequality Problems

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