求解变分不等式的一种双投影算法

Abstract

Abstract:

In this paper, we introduce a new method for solving variational inequalities. The method uses a new hyperplane which differs from known ones. Under some mild conditions, we prove that the sequence produced by our method globally converges to a solution. Furthermore, the convergence rate of the iteration sequence is established. Numerical experiments are reported in section 5.

Key words: Variational inequalities, Double projection method, Hyperplane, Convergence

CLC Number:

Yuxian Hu. A Double Projection Method for Solving Variational Inequalities[J].Acta mathematica scientia,Series A, 2019, 39(6): 1492-1498.

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References 10

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算法3.1			[6]算法2.2
n	iter	nf	time	iter	nf	time
n=10	22	45	0.296402	19	97	0.639604
n=50	27	55	0.514803	24	121	0.826805
n=100	29	59	2.58962	19	97	2.99522
n=200	35	71	4.19643	45	227	7.80005
n=500	33	67	15.7717	509	2547	197.684

算法3.1			[6]算法2.2
n	iter	nf	time	iter	nf	time
n=10	27	55	0.374402	28	141	0.686404
n=50	31	63	0.499203	25	126	0.748805
n=100	33	67	2.87042	19	96	3.12002
n=200	35	71	4.77363	23	116	4.83603
n=500	38	77	18.8449	448	2241	185.048

算法3.1			[10]算法3.1
x₀	iter	nf	time	iter	nf	time
(1, 1, 1, 1)	29	88	0.670804	140	425	1.65361
(0.5, 0.5, 2, 1)	34	103	0.780005	112	337	1.57561
(0.3, 0.3, 1.6, 1.8)	25	76	0.780005	177	539	2.12161
(1.6, 0.4, 1.3, 0.7)	31	94	0.733205	30	94	0.748805

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A Double Projection Method for Solving Variational Inequalities

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