A Novel Inertial Projection and Contraction Method for Solving Pseudomonotone Variational Inequality Problems

2019 ◽  
Vol 169 (1) ◽  
pp. 217-245 ◽  
Author(s):  
Prasit Cholamjiak ◽  
Duong Viet Thong ◽  
Yeol Je Cho
Keyword(s):  
Variational Inequality ◽  
Variational Inequality Problems ◽  
Contraction Method ◽  
Projection And Contraction Method

scholarly journals Improved inertial projection and contraction method for solving pseudomonotone variational inequality problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ming Tian ◽  
Gang Xu
Keyword(s):  
Variational Inequality ◽  
Real Hilbert Space ◽  
Lipschitz Constant ◽  
Variational Inequality Problems ◽  
Iterative Sequence ◽  
Step Size ◽  
Contraction Method ◽  
Projection And Contraction Method ◽  
Inertial Algorithm ◽  
Adaptive Step

AbstractThe objective of this article is to solve pseudomonotone variational inequality problems in a real Hilbert space. We introduce an inertial algorithm with a new self-adaptive step size rule, which is based on the projection and contraction method. Only one step projection is used to design the proposed algorithm, and the strong convergence of the iterative sequence is obtained under some appropriate conditions. The main advantage of the algorithm is that the proof of convergence of the algorithm is implemented without the prior knowledge of the Lipschitz constant of cost operator. Numerical experiments are also put forward to support the analysis of the theorem and provide comparisons with related algorithms.

Projection and Contraction Method for the Valuation of American Options

2015 ◽  
Vol 5 (1) ◽  
pp. 48-60 ◽  
Author(s):  
Haiming Song ◽  
Ran Zhang
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Variational Inequality ◽  
American Options ◽  
Superior Performance ◽  
Contraction Method ◽  
Projection And Contraction Method ◽  
Black Scholes ◽  
The Matrix ◽  
Element Method

AbstractAn efficient numerical method is proposed for the valuation of American options via the Black-Scholes variational inequality. A far field boundary condition is employed to truncate the unbounded domain problem to produce the bounded domain problem with the associated variational inequality, to which our finite element method is applied. We prove that the matrix involved in the finite element method is symmetric and positive definite, and solve the discretized variational inequality by the projection and contraction method. Numerical experiments are conducted that demonstrate the superior performance of our method, in comparison with earlier methods.

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