Variational Inequalities and Eigenvalue Problems for Nonlinear Maximal Monotone Operators in a Hilbert Space

1975 ◽  
Vol 97 (4) ◽  
pp. 905 ◽  
Author(s):  
Joao-Paulo Dias
Keyword(s):  
Hilbert Space ◽  
Variational Inequalities ◽  
Eigenvalue Problems ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Nonlinear Maximal Monotone

scholarly journals On an Iterative Method for Finding a Zero to the Sum of Two Maximal Monotone Operators

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Hongwei Jiao ◽  
Fenghui Wang
Keyword(s):  
Weak Convergence ◽  
Iterative Method ◽  
Variational Inequalities ◽  
Splitting Method ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Gradient Projection ◽  
Projection Algorithms

In this paper we consider a problem that consists of finding a zero to the sum of two monotone operators. One method for solving such a problem is the forward-backward splitting method. We present some new conditions that guarantee the weak convergence of the forward-backward method. Applications of these results, including variational inequalities and gradient projection algorithms, are also considered.

scholarly journals Differential game with switching controls on Hilbert space

1997 ◽  
Vol 39 (2) ◽  
pp. 230-256
Author(s):  
Siu Pang Yung
Keyword(s):  
Hilbert Space ◽  
Differential Game ◽  
Viscosity Solution ◽  
Real Hilbert Space ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Evolution System ◽  
Value Of The Game ◽  
Existence Of Value

AbstractWe study differential game problems in which the players can select different maximal monotone operators for the governing evolution system. Setting up our problem on a real Hilbert space, we show that the Elliott-Kalton upper and lower value of the game are viscosity solution of some Hamilton-Jacobi-Isaacs equations. Uniqueness is obtained by assuming condition analogous to the classical Isaacs condition, and thus the existence of value of the game follows.

scholarly journals Strong Convergence Theorems for Maximal Monotone Operators with Nonspreading Mappings in a Hilbert Space

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Hongjie Liu ◽  
Junqing Wang ◽  
Qiansheng Feng
Keyword(s):  
Hilbert Space ◽  
Strong Convergence ◽  
Monotone Mapping ◽  
Maximal Monotone ◽  
Iterative Algorithms ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Common Element ◽  
Convergence Theorems ◽  
Nonspreading Mappings

We prove the strong convergence theorems for finding a common element of the set of fixed points of a nonspreading mappingTand the solution sets of zero of a maximal monotone mapping and anα-inverse strongly monotone mapping in a Hilbert space. Manaka and Takahashi (2011) proved weak convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space; there we introduced new iterative algorithms and got some strong convergence theorems for maximal monotone operators with nonspreading mappings in a Hilbert space.

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