An inertial modified algorithm for solving variational inequalities
RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 1, pp. 163-178.

The paper deals with an inertial-like algorithm for solving a class of variational inequality problems involving Lipschitz continuous and strongly pseudomonotone operators in Hilbert spaces. The presented algorithm can be considered a combination of the modified subgradient extragradient-like algorithm and inertial effects. This is intended to speed up the convergence properties of the algorithm. The main feature of the new algorithm is that it is done without the prior knowledge of the Lipschitz constant and the modulus of strong pseudomonotonicity of the cost operator. Several experiments are performed to illustrate the convergence and computational performance of the new algorithm in comparison with others having similar features. The numerical results have confirmed that the proposed algorithm has a competitive advantage over the existing methods.

DOI : 10.1051/ro/2018115
Classification : 65J15, 47H05, 47J25, 47J20, 91B50
Mots-clés : Modified extragradient method, inertial effect, variational inequality, pseudomonotone operator, Lipschitz continuity 
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     title = {An inertial modified algorithm for solving variational inequalities},
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     pages = {163--178},
     publisher = {EDP-Sciences},
     volume = {54},
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     year = {2020},
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     mrnumber = {4052235},
     zbl = {1516.65050},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro/2018115/}
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Hieu, Dang Van; Quy, Pham Kim. An inertial modified algorithm for solving variational inequalities. RAIRO - Operations Research - Recherche Opérationnelle, Tome 54 (2020) no. 1, pp. 163-178. doi : 10.1051/ro/2018115. http://www.numdam.org/articles/10.1051/ro/2018115/

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