Inertial modified projection algorithm with self-adaptive technique for solving pseudo-monotone variational inequality problems in Hilbert spaces

The alternating directions method for a kind of structured variational inequality problem (He, 2001) is an attractive method for structured monotone variational inequality problems. In each iteration, the subproblemsare convex quadratic minimization problem with simple constraintsand a well-conditioned system of nonlinear equations that can be efficiently solvedusing classical methods. Researchers have recently described the convergence rateof projection and contraction methods for variational inequality problems andthe original ADM and its linearized variant. Motivated and inspired by researchinto the convergence rate of these methods, we provide a simple proof to show the $O(1/k)$ convergencerate of alternating directions methods for structured monotone variational inequality problems (He, 2001).

Download Full-text

Self adaptive inertial subgradient extragradient algorithms for solving pseudomonotone variational inequality problems

Optimization Letters ◽

10.1007/s11590-019-01511-z ◽

2019 ◽

Vol 14 (1) ◽

pp. 115-144 ◽

Cited By ~ 5

Author(s):

Duong Viet Thong ◽

Dang Van Hieu ◽

Themistocles M. Rassias

Keyword(s):

Variational Inequality ◽

Variational Inequality Problems ◽

Self Adaptive

Download Full-text

An Extended Projection Neural Network for Constrained Optimization

Neural Computation ◽

10.1162/089976604322860730 ◽

2004 ◽

Vol 16 (4) ◽

pp. 863-883 ◽

Cited By ~ 102

Author(s):

Youshen Xia

Keyword(s):

Neural Network ◽

Variational Inequality ◽

Parallel Implementation ◽

Variational Inequality Problems ◽

Extended Projection ◽

Linear And Nonlinear Constraints ◽

Lower Complexity ◽

Monotone Variational Inequality ◽

Projection Neural Network ◽

Special Case

Recently, a projection neural network has been shown to be a promising computational model for solving variational inequality problems with box constraints. This letter presents an extended projection neural network for solving monotone variational inequality problems with linear and nonlinear constraints. In particular, the proposed neural network can include the projection neural network as a special case. Compared with the modified projection-type methods for solving constrained monotone variational inequality problems, the proposed neural network has a lower complexity and is suitable for parallel implementation. Furthermore, the proposed neural network is theoretically proven to be exponentially convergent to an exact solution without a Lipschitz condition. Illustrative examples show that the extended projection neural network can be used to solve constrained monotone variational inequality problems.

Download Full-text

A Parallel-Viscosity-Type Subgradient Extragradient-Line Method for Finding the Common Solution of Variational Inequality Problems Applied to Image Restoration Problems

Mathematics ◽

10.3390/math8020248 ◽

2020 ◽

Vol 8 (2) ◽

pp. 248 ◽

Cited By ~ 2

Author(s):

Suthep Suantai ◽

Pronpat Peeyada ◽

Damrongsak Yambangwai ◽

Watcharaporn Cholamjiak

Keyword(s):

Variational Inequality ◽

Hilbert Spaces ◽

Hybrid Algorithm ◽

Variational Inequality Problems ◽

Strong Convergence Theorem ◽

Infinite Dimensional ◽

Common Solution ◽

Line Method ◽

The Common ◽

Monotone Hybrid Algorithm

In this paper, we study a modified viscosity type subgradient extragradient-line method with a parallel monotone hybrid algorithm for approximating a common solution of variational inequality problems. Under suitable conditions in Hilbert spaces, the strong convergence theorem of the proposed algorithm to such a common solution is proved. We then give numerical examples in both finite and infinite dimensional spaces to justify our main theorem. Finally, we can show that our proposed algorithm is flexible and has good quality for use with common types of blur effects in image recovery.

Download Full-text