Journal
ACTA APPLICANDAE MATHEMATICAE
Volume 170, Issue 1, Pages 981-1064Publisher
SPRINGER
DOI: 10.1007/s10440-020-00366-2
Keywords
Variational inequalities; Wiener-Hopf equations; Dynamical systems; Equilibrium problems
Categories
Funding
- University of Zurich
Ask authors/readers for more resources
It is well known that general variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of unrelated problems, which arise in pure and applied sciences. In this paper, we present a number of new and known numerical techniques for solving general variational inequalities and equilibrium problems using various techniques including projection, Wiener-Hopf equations, dynamical systems, the auxiliary principle and the penalty function. General variational-like inequalities are introduced and investigated. Properties of higher order strongly general convex functions have been discussed. The auxiliary principle technique is used to suggest and analyze some iterative methods for solving higher order general variational inequalities. Some new classes of strongly exponentially general convex functions are introduced and discussed. Our proofs of convergence are very simple as compared with other methods. Our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems. Since the general variational inequalities include (quasi) variational inequalities and (quasi) implicit complementarity problems as special cases, these results continue to hold for these problems. Some numerical results are included to illustrate the efficiency of the proposed methods. Several open problems have been suggested for further research in these areas.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available