Uniqueness of supporting hyperplanes and an alternative to solutions of variational inequalities

Authors:
Songnian He;Hong-Kun Xu
Affiliations:
College of Science, Civil Aviation University of China, Tianjin, China 300300;Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung, Taiwan 80424
Venue:
Journal of Global Optimization
Year:
2013

Citing 3
Cited 0

Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications

Mathematical Programming: Series A and B
Equivalent differentiable optimization problems and descent methods for asymmetric variational inequality problems

Mathematical Programming: Series A and B
Improvements of some projection methods for monotone nonlinear variational inequalities

Journal of Optimization Theory and Applications

Quantified Score

Hi-index	0.00

Visualization

Abstract

A uniqueness 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. Three examples are given to demonstrate the usefulness and advantages of our alternative theorem.