April  2005, 1(2): 211-217. doi: 10.3934/jimo.2005.1.211

The revisit of a projection algorithm with variable steps for variational inequalities

1. 

School of Mathematics and LPMC, Nankai University, Tianjin 300071, P.R., China

Received  August 2004 Revised  January 2005 Published  April 2005

The projection-type methods are a class of important methods for solving variational inequalities(VI). This paper presents a new treatment to a classical projection algorithm with variable steps, which was first proposed by Auslender in 1970s and later was developed by Fukushima in 1980s. The main purpose of this work is to weaken the assumption conditions while the convergence of original method is still valid.
Citation: Qingzhi Yang. The revisit of a projection algorithm with variable steps for variational inequalities. Journal of Industrial and Management Optimization, 2005, 1 (2) : 211-217. doi: 10.3934/jimo.2005.1.211
[1]

Ouafa Belguidoum, Hassina Grar. An improved projection algorithm for variational inequality problem with multivalued mapping. Numerical Algebra, Control and Optimization, 2022  doi: 10.3934/naco.2022002

[2]

Abd-semii Oluwatosin-Enitan Owolabi, Timilehin Opeyemi Alakoya, Adeolu Taiwo, Oluwatosin Temitope Mewomo. A new inertial-projection algorithm for approximating common solution of variational inequality and fixed point problems of multivalued mappings. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 255-278. doi: 10.3934/naco.2021004

[3]

Yazheng Dang, Fanwen Meng, Jie Sun. Convergence analysis of a parallel projection algorithm for solving convex feasibility problems. Numerical Algebra, Control and Optimization, 2016, 6 (4) : 505-519. doi: 10.3934/naco.2016023

[4]

Xueling Zhou, Meixia Li, Haitao Che. Relaxed successive projection algorithm with strong convergence for the multiple-sets split equality problem. Journal of Industrial and Management Optimization, 2021, 17 (5) : 2557-2572. doi: 10.3934/jimo.2020082

[5]

Yan Tang. Convergence analysis of a new iterative algorithm for solving split variational inclusion problems. Journal of Industrial and Management Optimization, 2020, 16 (2) : 945-964. doi: 10.3934/jimo.2018187

[6]

Grace Nnennaya Ogwo, Chinedu Izuchukwu, Oluwatosin Temitope Mewomo. A modified extragradient algorithm for a certain class of split pseudo-monotone variational inequality problem. Numerical Algebra, Control and Optimization, 2022, 12 (2) : 373-393. doi: 10.3934/naco.2021011

[7]

Liping Pang, Fanyun Meng, Jinhe Wang. Asymptotic convergence of stationary points of stochastic multiobjective programs with parametric variational inequality constraint via SAA approach. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1653-1675. doi: 10.3934/jimo.2018116

[8]

Takeshi Fukao. Variational inequality for the Stokes equations with constraint. Conference Publications, 2011, 2011 (Special) : 437-446. doi: 10.3934/proc.2011.2011.437

[9]

Zijia Peng, Cuiming Ma, Zhonghui Liu. Existence for a quasistatic variational-hemivariational inequality. Evolution Equations and Control Theory, 2020, 9 (4) : 1153-1165. doi: 10.3934/eect.2020058

[10]

S. J. Li, Z. M. Fang. On the stability of a dual weak vector variational inequality problem. Journal of Industrial and Management Optimization, 2008, 4 (1) : 155-165. doi: 10.3934/jimo.2008.4.155

[11]

Junkee Jeon, Jehan Oh. Valuation of American strangle option: Variational inequality approach. Discrete and Continuous Dynamical Systems - B, 2019, 24 (2) : 755-781. doi: 10.3934/dcdsb.2018206

[12]

Thanyarat JItpeera, Tamaki Tanaka, Poom Kumam. Triple-hierarchical problems with variational inequality. Numerical Algebra, Control and Optimization, 2021  doi: 10.3934/naco.2021038

[13]

Elena Beretta, Markus Grasmair, Monika Muszkieta, Otmar Scherzer. A variational algorithm for the detection of line segments. Inverse Problems and Imaging, 2014, 8 (2) : 389-408. doi: 10.3934/ipi.2014.8.389

[14]

Jaakko Ketola, Lars Lamberg. An algorithm for recovering unknown projection orientations and shifts in 3-D tomography. Inverse Problems and Imaging, 2011, 5 (1) : 75-93. doi: 10.3934/ipi.2011.5.75

[15]

Yazheng Dang, Marcus Ang, Jie Sun. An inertial triple-projection algorithm for solving the split feasibility problem. Journal of Industrial and Management Optimization, 2022  doi: 10.3934/jimo.2022019

[16]

Micol Amar, Andrea Braides. A characterization of variational convergence for segmentation problems. Discrete and Continuous Dynamical Systems, 1995, 1 (3) : 347-369. doi: 10.3934/dcds.1995.1.347

[17]

A. Pedas, G. Vainikko. Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Communications on Pure and Applied Analysis, 2006, 5 (2) : 395-413. doi: 10.3934/cpaa.2006.5.395

[18]

J. Frédéric Bonnans, Justina Gianatti, Francisco J. Silva. On the convergence of the Sakawa-Shindo algorithm in stochastic control. Mathematical Control and Related Fields, 2016, 6 (3) : 391-406. doi: 10.3934/mcrf.2016008

[19]

Masao Fukushima. A class of gap functions for quasi-variational inequality problems. Journal of Industrial and Management Optimization, 2007, 3 (2) : 165-171. doi: 10.3934/jimo.2007.3.165

[20]

Wenyan Zhang, Shu Xu, Shengji Li, Xuexiang Huang. Generalized weak sharp minima of variational inequality problems with functional constraints. Journal of Industrial and Management Optimization, 2013, 9 (3) : 621-630. doi: 10.3934/jimo.2013.9.621

2020 Impact Factor: 1.801

Metrics

  • PDF downloads (103)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]