A relaxed projection method for variational inequalities
Mathematical Programming: Series A and B
Modified Projection-Type Methods for Monotone Variational Inequalities
SIAM Journal on Control and Optimization
Solving nonlinear multicommodity flow problems by the analytic center cutting plane method
Mathematical Programming: Series A and B - Special issue: interior point methods in theory and practice
On a Primal-Dual Analytic Center Cutting Plane Method for VariationalInequalities
Computational Optimization and Applications - Special issue on computational optimization—a tribute to Olvi Mangasarian, part I
Origin-Based Algorithm for the Traffic Assignment Problem
Transportation Science
An analytic center cutting plane method for pseudomonotone variational inequalities
Operations Research Letters
Column generation algorithms for nonlinear optimization, II: Numerical investigations
Computers and Operations Research
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The purpose of the traffic assignment problem is to obtain a traffic flow pattern given a set of origin-destination travel demands and flow dependent link performance functions of a road network. In the general case, the traffic assignment problem can be formulated as a variational inequality, and several algorithms have been devised for its efficient solution. In this work we propose a new approach that combines two existing procedures: the master problem of a simplicial decomposition algorithm is solved through the analytic center cutting plane method. Four variants are considered for solving the master problem. The third and fourth ones, which heuristically compute an appropriate initial point, provided the best results. The computational experience reported in the solution of real large-scale diagonal and difficult asymmetric problems--including a subset of the transportation networks of Madrid and Barcelona--show the effectiveness of the approach.