Equilibrium algorithms with nonmonotone line search technique for solving traffic assignment problems

This paper presents a unified framework of nonmonotone convex combination algorithms (such as Frank–Wolfe Algorithm) for solving traffic assignment problems. Global convergence results are established under mild conditions. The line search procedure used in our algorithm includes the nonmonotone Armijo rule, the nonmonotone Goldstein rule and the nonmonotone Wolfe rule as special cases. So, the new algorithm can be viewed as a generalization of the regular convex combination algorithm.