Some Predictor-Corrector Algorithms for Multivalued Variational Inequalities

2001 ◽  
Vol 108 (3) ◽  
pp. 659-670 ◽  
Author(s):  
M. A. Noor
Keyword(s):  
Variational Inequalities ◽  
Predictor Corrector ◽  
Multivalued Variational Inequalities

scholarly journals On a class of multivalued variational inequalities

1998 ◽  
Vol 11 (1) ◽  
pp. 79-93 ◽  
Author(s):  
Muhammad Aslam Noor
Keyword(s):  
Variational Inequalities ◽  
Optimization Problems ◽  
Iterative Algorithms ◽  
Auxiliary Principle ◽  
Existence Of A Solution ◽  
Auxiliary Principle Technique ◽  
New Class ◽  
Special Cases ◽  
Projection Techniques ◽  
Multivalued Variational Inequalities

In this paper, we introduce and study a new class of variational inequalities, which are called multivalued variational inequalities. These variational inequalities include as special cases, the previously known classes of variational inequalities. Using projection techniques, we show that multivalued variational inequalities are equivalent to fixed point problems and Wiener-Hopf equations. These alternate formulations are used to suggest a number of iterative algorithms for solving multivalued variational inequalities. We also consider the auxiliary principle technique to study the existence of a solution of multivalued variational inequalities and suggest a novel iterative algorithm. In addition, we have shown that the auxiliary principle technique can be used to find the equivalent differentiable optimization problems for multivalued variational inequalities. Convergence analysis is also discussed.

scholarly journals A Predictor-Corrector Method for Solving Equilibrium Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Zong-Ke Bao ◽  
Ming Huang ◽  
Xi-Qiang Xia
Keyword(s):  
Variational Inequalities ◽  
Convergence Analysis ◽  
Equilibrium Problems ◽  
Auxiliary Problem ◽  
The Other ◽  
Stationary Points ◽  
Stopping Criterion ◽  
Auxiliary Problem Principle ◽  
One Step ◽  
Predictor Corrector

We suggest and analyze a predictor-corrector method for solving nonsmooth convex equilibrium problems based on the auxiliary problem principle. In the main algorithm each stage of computation requires two proximal steps. One step serves to predict the next point; the other helps to correct the new prediction. At the same time, we present convergence analysis under perfect foresight and imperfect one. In particular, we introduce a stopping criterion which gives rise toΔ-stationary points. Moreover, we apply this algorithm for solving the particular case: variational inequalities.

Sign in / Sign up

Export Citation Format

Share Document