EconPapers    
Economics at your fingertips  
 

Regularizations for Stochastic Linear Variational Inequalities

Yanfang Zhang () and Xiaojun Chen ()
Additional contact information
Yanfang Zhang: Chinese Academy of Sciences
Xiaojun Chen: The Hong Kong Polytechnic University

Journal of Optimization Theory and Applications, 2014, vol. 163, issue 2, No 6, 460-481

Abstract: Abstract This paper applies the Moreau–Yosida regularization to a convex expected residual minimization (ERM) formulation for a class of stochastic linear variational inequalities. To have the convexity of the corresponding sample average approximation (SAA) problem, we adopt the Tikhonov regularization. We show that any cluster point of minimizers of the Tikhonov regularization for the SAA problem is a minimizer of the ERM formulation with probability one as the sample size goes to infinity and the Tikhonov regularization parameter goes to zero. Moreover, we prove that the minimizer is the least $$l_2$$ l 2 -norm solution of the ERM formulation. We also prove the semismoothness of the gradient of the Moreau–Yosida and Tikhonov regularizations for the SAA problem.

Keywords: Stochastic variational inequality; Epi-convergence; Semismooth; Expected residual minimization; Sample average approximations; 90C33; 90C15 (search for similar items in EconPapers)
Date: 2014
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://link.springer.com/10.1007/s10957-013-0514-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-013-0514-2

Ordering information: This journal article can be ordered from
http://www.springer. ... cs/journal/10957/PS2

DOI: 10.1007/s10957-013-0514-2

Access Statistics for this article

Journal of Optimization Theory and Applications is currently edited by Franco Giannessi and David G. Hull

More articles in Journal of Optimization Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().

 
Page updated 2025-03-20
Handle: RePEc:spr:joptap:v:163:y:2014:i:2:d:10.1007_s10957-013-0514-2