关于伪单调变分不等式与不动点问题的新投影算法

Abstract

Abstract:

In this paper, we propose a new projection algorithm for finding a common element of psedomonotone variational inequality problems and fixed point set of demicontractive mappings in Hilbert spaces. We prove that this new algorithm converges strongly to the common element for a psedomonotone and uniformly continuous mapping. Finally, we provide some numerical experiments to illustrate the efficiency and advantages of the new projection algorithm.

Key words: Variational inequality, Fixed point, Projection algorithm, Uniformly continuous, Pseudomonotone

CLC Number:

O224

Jing Yang,Xianjun Long. A New Projection Algorithm for Solving Pseudo-Monotone Variational Inequality and Fixed Point Problems[J].Acta mathematica scientia,Series A, 2022, 42(3): 904-919.

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Figures/Tables 12

References 21

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$f(x)$	$m=30$		$m=60$		$m=90$
$f(x)$	Iter	CPU time	Iter	CPU time	Iter	GPU time
$\frac{x}{4}$	51	0.8511	52	0.7227	52	0.7869
$\frac{x}{2}$	53	0.7082	58	0.8453	62	0.9145
$\frac{\sin(x)}{2}$	55	0.7157	53	0.6831	57	0.9798
$\frac{\cos(x)}{2}$	236	5.7441	318	9.4689	427	19.516

$err=10^{-8}$	$m=50$		$m=60$		$m=70$
$err=10^{-8}$	Iter	CPU time	Iter	CPU time	Iter	CPU time
Alg 3.1	41	0.3043	42	0.3151	42	0.9606
Alg 1 in [8]	136	0.9405	145	0.9811	1902	38.337
Alg 2 in [8]	329	2.5770	490	3.7967	527	4.3241
Alg 4 in [7]	237	3.2041	533	9.0855	6513	106.62

$err$	Alg.3.1		Alg.3.2 in [12]		Alg.3.1 in [12]
$err$	Iter	CPU time	Iter	CPU time	Iter	GPU time
$10^{-10}$	12	0.0144	17	0.0239	24868	0.2387
$10^{-12}$	14	0.0154	19	0.0243	$\geq 10^{6}$	1.7069
$10^{-14}$	16	0.0165	22	0.0297	$\geq 10^{7}$	15.944

	$10^{-5}$		$10^{-10}$		$10^{-15}$
	Iter	CPU time	Iter	CPU time	Iter	GPU time
Alg 3.1	28	0.0138	66	0.0163	104	0.0529
Alg 1 in [8]	39	0.0238	80	0.0274	120	0.0635
Alg 2 in [8]	45	0.0257	126	0.0357	207	0.0933
Alg 3.1 in [13]	42	0.0142	86	0.0175	127	0.0548

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A New Projection Algorithm for Solving Pseudo-Monotone Variational Inequality and Fixed Point Problems

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