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Stochastic traffic assignment, Lagrangian dual, and unconstrained convex optimization

机译：随机交通分配，拉格朗日对偶和无约束凸优化

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In this paper, traffic assignment problems with stochastic travel cost perceptions are refor-mulated and investigated in a new unconstrained nonlinear programming formulation. The objective function of the unconstrained formulation consists of two terms, in which the first term specifies the routing principle of the target problem through a satisfaction func-tion and the sum of the first and second terms denotes the system cost or optimization objective. This formulation proves to be the Lagrangian dual of a generic primal formula-tion proposed by Maher et al. (2005) for the stochastic system-optimal problem. The pri-mal-dual modeling framework presents such a common functional form that can accommodate a wide range of different traffic assignment problems. Our particular atten-tion is given to the dual formulation in that its unconstrained feature opens the door of applying unconstrained optimization algorithms for its embraced traffic assignment prob-lems. Numerical examples are provided to support the insights and facts derived from applying the primal and dual formulations to model stochastic system-optimal and user-equilibrium problems and justify the conjugate relationship between the primal and dual models.
机译：在本文中，以新的无约束非线性规划公式对具有随机旅行成本感知的交通分配问题进行了重新计算和研究。无约束公式的目标函数由两个术语组成，其中第一个术语通过满意度函数指定目标问题的路由原理，而第一和第二个术语的总和表示系统成本或优化目标。该公式被证明是Maher等人提出的通用原始公式的Lagrangian对偶。 （2005年）为随机系统最优问题。双向建模框架提供了一种通用的功能形式，可以适应各种不同的交通分配问题。我们特别关注双重表示法，因为它的不受约束的特征为对其包含的交通分配问题应用不受约束的优化算法打开了大门。提供了数值示例，以支持将原始和对偶公式应用到随机系统最优和用户均衡问题建模中的见解和事实，并证明原始和对偶模型之间的共轭关系是正确的。

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