解变分不等式的一种二次投影算法

Abstract

Abstract:

In this paper, a new double projection algorithm for solving variational inequalities is proposed. By constructing a new class of hyperplanes that strictly separate the current iteration and variational inequality solution sets and improving proof of existing results, We prove that the infinite sequence generated by the algorithm is globally convergent, and establish the convergence rate analysis under local error and Lipschitz conditions.

Key words: Variational inequalities, Double projection algorithm, Hyperplanes, Pseudomonotone, Convergence

CLC Number:

Shenglian Wan. A Double Projection Algorithm for Solving Variational Inequalities[J].Acta mathematica scientia,Series A, 2021, 41(1): 237-244.

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References 16

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	算法3.1.1	算法3.1.2	算法2.2
n	iter(nf) time	iter(nf) time	iter(nf) time
n = 10	14(64) 0.561604	14(65) 0.546004	22(87) 0.748805
n = 50	17(79) 0.639604	17(83) 0.608404	20(85) 0.670804
n = 100	19(89) 1.48201	17(81) 1.37281	21(85) 1.62241
n = 200	18(86) 2.35562	18(85) 2.46482	22(89) 2.13721
n = 500	19(87) 9.21966	18(87) 9.15726	23(93) 8.04965

	算法3.1.1	算法3.1.2	算法2.2
n	iter(nf) time	iter(nf) time	iter(nf) time
n = 10	17(76) 0.421203	16(72) 0.499203	18(69) 0.499203
n = 50	19(90) 0.483603	19(95) 0.483603	20(78) 0.624004
n = 100	20(95) 1.201210	19(93) 1.232410	21(82) 1.23241
n = 200	20(96) 2.090410	20(98) 1.996810	21(89) 2.12161
n = 500	20(95) 9.762660	20(95) 10.43650	21(98) 6.70804

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A Double Projection Algorithm for Solving Variational Inequalities

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