The supporting hyperplane and an alternative to solutions of variational inequalities

Huu Quang Nguyen, Hong Kun Xu

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Two examples are given to demonstrate the usefulness and advantages of our alternative theorem.

Original languageEnglish
Pages (from-to)2323-2331
Number of pages9
JournalJournal of Nonlinear and Convex Analysis
Volume16
Issue number11
Publication statusPublished - 2015 Jan 1

Fingerprint

Alternative Theorems
Hilbert spaces
Level Set
Hyperplane
Convex Sets
Variational Inequalities
Alternatives
Hilbert space
Theorem
Demonstrate
Class

All Science Journal Classification (ASJC) codes

  • Analysis
  • Geometry and Topology
  • Control and Optimization
  • Applied Mathematics

Cite this

@article{a2ec5af49f4f427bafcff5ee911f70b9,
title = "The supporting hyperplane and an alternative to solutions of variational inequalities",
abstract = "A theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Two examples are given to demonstrate the usefulness and advantages of our alternative theorem.",
author = "Nguyen, {Huu Quang} and Xu, {Hong Kun}",
year = "2015",
month = "1",
day = "1",
language = "English",
volume = "16",
pages = "2323--2331",
journal = "Journal of Nonlinear and Convex Analysis",
issn = "1345-4773",
publisher = "Yokohama Publishers",
number = "11",

}

The supporting hyperplane and an alternative to solutions of variational inequalities. / Nguyen, Huu Quang; Xu, Hong Kun.

In: Journal of Nonlinear and Convex Analysis, Vol. 16, No. 11, 01.01.2015, p. 2323-2331.

Research output: Contribution to journalArticle

TY - JOUR

T1 - The supporting hyperplane and an alternative to solutions of variational inequalities

AU - Nguyen, Huu Quang

AU - Xu, Hong Kun

PY - 2015/1/1

Y1 - 2015/1/1

N2 - A theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Two examples are given to demonstrate the usefulness and advantages of our alternative theorem.

AB - A theorem of supporting hyperplanes for a class of convex level sets in a Hilbert space is obtained. As an application of this result, we prove an alternative theorem on solutions of variational inequalities defined on convex level sets. Two examples are given to demonstrate the usefulness and advantages of our alternative theorem.

UR - http://www.scopus.com/inward/record.url?scp=84954088598&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84954088598&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:84954088598

VL - 16

SP - 2323

EP - 2331

JO - Journal of Nonlinear and Convex Analysis

JF - Journal of Nonlinear and Convex Analysis

SN - 1345-4773

IS - 11

ER -