The convergence of equilibrium algorithms with non-monotone line search technique

The slow-convergence characteristics of the regular convex combination algorithm (such as Frank-Wolfe method) are well known particularly when the optimal solution is being reached. In this paper, a new convex combination algorithm with non-monotone line search technique proposed for solving the equilibrium assignment problem, together with the proof of its global convergence. Moreover, it should-be pointed out that the conditions which ensure the global convergence of the algorithm proposed in this paper are much milder than those suggested by Bonnans et al.,- Grippo et al.; Panier andTits; Xu et al. [SIAM J. Number. Anal. 29 (4) (1992) 1187; SIAM J. Number. Anal. 23 (4) (1986) 707; SIAM J. Number. Anal. 28 (4) (1991) 1183; Comput. Optimiz. Appl. 18 (2001) 221]. The new algorithm can be viewed as a generalization of the regular convex combination algorithm. Numerical results indicate that the,proposed algorithm would lead to a considerable saving both in the number of line searches and in the number of function evaluations. (C) 2002 Elsevier Inc. All rights reserved.