A smoothing inexact Newton method for variational inequality problems

2011 ◽  
Vol 88 (6) ◽  
pp. 1283-1293 ◽  
Author(s):  
Xiuyun Zheng ◽  
Hongwei Liu
Keyword(s):  
Variational Inequality ◽  
Newton Method ◽  
Variational Inequality Problems ◽  
Inexact Newton Method

A Hybrid Newton Method for Stochastic Variational Inequality Problems and Application to Traffic Equilibrium

2020 ◽  
pp. 2050036
Author(s):  
Yan-Chao Liang ◽  
Qiao-Na Fan ◽  
Pei-Ping Shen
Keyword(s):  
Variational Inequality ◽  
Newton Method ◽  
Sample Average Approximation ◽  
Gap Function ◽  
Variational Inequality Problems ◽  
Traffic Equilibrium ◽  
Stochastic Variational Inequality ◽  
Sample Average ◽  
Optimization Reformulation ◽  
Average Approximation

In this paper, we consider a class of stochastic variational inequality problems (SVIPs). Different from the classical variational inequality problems, the SVIP contains a mathematical expectation, which may not be evaluated in an explicit form in general. We combine a hybrid Newton method for deterministic cases with an unconstrained optimization reformulation based on the well-known D-gap function and sample average approximation (SAA) techniques to present an SAA-based hybrid Newton method for solving the SVIP. We show that the level sets of the approximation D-gap function are bounded. Furthermore, we prove that the sequence generated by the hybrid Newton method converges to a solution of the SVIP under appropriate conditions, and some numerical experiments are presented to prove the effectiveness and competitiveness of the hybrid Newton method. Finally, we apply this method to solve two specific traffic equilibrium problems.

Electromagnetic subsurface prospecting by a fully nonlinear multifocusing inexact Newton method

2014 ◽  
Vol 31 (12) ◽  
pp. 2618 ◽  
Author(s):  
Marco Salucci ◽  
Giacomo Oliveri ◽  
Andrea Randazzo ◽  
Matteo Pastorino ◽  
Andrea Massa
Keyword(s):  
Newton Method ◽  
Inexact Newton Method ◽  
Fully Nonlinear
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