skip to main content
US FlagAn official website of the United States government
dot gov icon
Official websites use .gov
A .gov website belongs to an official government organization in the United States.
https lock icon
Secure .gov websites use HTTPS
A lock ( lock ) or https:// means you've safely connected to the .gov website. Share sensitive information only on official, secure websites.


Title: Inverse problems for multi-valued quasi variational inequalities and noncoercive variational inequalities with noisy data
Award ID(s):
1720067
PAR ID:
10096219
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Optimization
ISSN:
0233-1934
Page Range / eLocation ID:
1 to 35
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. Motivated by structures that appear in deep neural networks, we investigate nonlinear com- posite models alternating proximity and affine operators defined on different spaces. We first show that a wide range of activation operators used in neural networks are actually proximity operators. We then establish conditions for the averagedness of the proposed composite constructs and investigate their asymptotic properties. It is shown that the limit of the resulting process solves a variational inequality which, in general, does not derive from a minimization problem. The analysis relies on tools from monotone operator theory and sheds some light on a class of neural networks structures with so far elusive asymptotic properties. 
    more » « less
  2. In this paper, we generalize the classical extragradient algorithm for solving variational inequality problems by utilizing nonzero normal vectors of the feasible set. In particular, conceptual algorithms are proposed with two different linesearchs. We then establish convergence results for these algorithms under mild assumptions. Our study suggests that nonzero normal vectors may significantly improve convergence if chosen appropriately. 
    more » « less