Daoli Zhu

Advances in the Continuous Dynamic Network Loading Problem

The continuous dynamic network loading problem (CDNLP) consists in determining, on a congested network, time-dependent arc volumes, together with arc and path travel times, given the time varying path flow departure rates over a finite time horizon. This problem constitutes an intrinsic part of the dynamic traffic assignment problem. In this paper, the authors present a formulation of the CDNLP where travel delays may be nonlinear functions of arc traffic volumes. They show, under a boundedness condition, that there exists a unique solution to the problem and propose for its solution a finite-step algorithm. Some computational results are reported for a discretized version of the algorithm.(A)

On the Existence of Solutions to the Dynamic User Equilibrium Problem

This paper is concerned with the existence of solutions to a dynamic network equilibrium problem modeled as an infinite dimensional variational inequality. Our results are based on properties of operators that map path flow departure rates to consistent time-dependent path flows and other link performance functions. The existence result requires the introduction of a novel concept that strengthens the familiar concept of First-In-First-Out (FIFO).

Weak Sharp Solutions of Variational Inequalities

Xuexiang Huang pointed out that the statement on line 5 of page 184 of [P. Marcotte and D. Zhu, SIAM J. Optim., 9 (1999), pp. 179--189] is invalid, and supplied an alternative proof of the inequality that appears on line 10. Here is a simple proof of this result due to an anonymous referee. The substitution starts at line 4 and ends at line 11.

Modified descent methods for solving the monotone variational inequality problem

Recently, Fukushima proposed a differentiable optimization framework for solving strictly monotone and continuously differentiable variational inequalities. The main result of this paper is to show that Fukushimas results can be extended to monotone (not necessarily strictly monotone) and Lipschitz continuous (not necessarily continuously differentiable) variational inequalities, if one is willing to modify slightly the basic algorithmic scheme. The modification applies also to a general descent scheme introduced by Zhu and Marcotte.

Conditions ensuring the applicability of cutting-plane methods for solving variational inequalities

Abstract.Let VIP(F,C) denote the variational inequality problem associated with the mapping F and the closed convex set C. In this paper we introduce weak conditions on the mapping F that allow the development of a convergent cutting-plane framework for solving VIP(F,C). In the process we introduce, in a natural way, new and useful notions of generalized monotonicity for which first order characterizations are presented.

An analytic center cutting plane method for pseudomonotone variational inequalities

We consider an analytic center algorithm for solving generalized monotone variational inequalities in R^n, which adapts a recent result due to Goffin et al. (1993) to the numerical resolution of continuous pseudomonotone variational inequalities.

Existence and computation of optimal tolls in multiclass network equilibrium problems

In this work we provide a simple proof of the existence of optimal tolls for multiclass network equilibrium problems where the value-of-time parameter varies continuously throughout the population. The main argument, based on a finite-dimensional reformulation of the problem, also allows us to determine in a simple fashion revenue minimizing link toll vectors.

Mathematical structure of a bilevel strategic pricing model

This paper is concerned with the characterization of optimal strategies for a service firm acting in an oligopolistic environment. The decision problem is formulated as a leader-follower game played on a transportation network, where the leader firm selects a revenue-maximizing price schedule that takes explicitly into account the rational behavior of the customers. In the context of our analysis, the followers problem is associated with a competitive network market involving non atomic customer groups. The resulting bilevel model can therefore be viewed as a model of product differentiation subject to structural network constraints.

A Cutting Plane Method for Solving Quasimonotone Variational Inequalities

We present an iterative algorithm for solving variational inequalities under the weakest monotonicity condition proposed so far. The method relies on a new cutting plane and on analytic centers.

An Efficient Algorithm for a Bicriterion Traffic Assignment Problem

We consider a bicriterion traffic assignment model where the network users have different values of time. We present an infinite-dimensional formulation of this model that lends itself to an extremely simple and efficient algorithm that takes into account the network structure of the problem.