New Parallel Descent-like Method for Solving a Class of Variational Inequalities
- 154 Downloads
To solve a class of variational inequalities with separable structures, some classical methods such as the augmented Lagrangian method and the alternating direction methods require solving two subvariational inequalities at each iteration. The most recent work (B.S. He in Comput. Optim. Appl. 42(2):195–212, 2009) improved these classical methods by allowing the subvariational inequalities arising at each iteration to be solved in parallel, at the price of executing an additional descent step. This paper aims at developing this strategy further by refining the descent directions in the descent steps, while preserving the practical characteristics suitable for parallel computing. Convergence of the new parallel descent-like method is proved under the same mild assumptions on the problem data.
KeywordsVariational inequalities Parallel computing Descent-like methods Alternating direction methods Augmented Lagrangian method
Unable to display preview. Download preview PDF.
- 2.Facchinei, F., Pang, J.S.: Finite-dimensional Variational Inequalities and Complementarity Problems, vols. I and II. Springer Series in Operations Research. Springer, New York (2003) Google Scholar
- 4.Giannessi, F., Maugeri, A., Pardalos, P.M.: Equilibrium Problems and Variational Models. Kluwer Academic, Dordrecht (2001) Google Scholar
- 5.Kinderlehrer, D., Stampacchia, G.: A Introduction to Variational Inequalities and Their Applications. Academic Press, New York (1980) Google Scholar
- 8.Eckstein, J., Fukushima, M.: Some reformulation and applications of the alternating direction method of multipliers. Large Scale Optimization: State of the Art, pp. 115–134. Kluwer Academic, Dordrecht (1994). Google Scholar
- 25.D’Apuzzo, M., Marino, M., Migdalas, A., Pardalos, P.M., Toraldo, G.: Parallel computing in global optimization. In: Handbook of Parallel Computing and Statistics, pp. 225–258. Chapman & Hall, London (2006) Google Scholar
- 28.Bertsekas, D.P., Gafni, E.M.: Projection method for variational inequalities with applications to the traffic assignment problem. Math. Program. Study 17 (1982) Google Scholar