相关论文: A Decomposition Method for Solving Multicommodity …
Markovian network equilibrium generalizes the classical Wardrop equilibrium in network games. At a Markovian network equilibrium, each player of the game solves a Markov decision process instead of a shortest path problem. We propose two…
We present a general two-side market model with divisible commodities and price functions of participants. A general existence result on unbounded sets is obtained from its variational inequality re-formulation. We describe an extension of…
We consider multi-commodity network design models, where capacity can be added to the arcs of the network using multiples of facilities that may have different capacities. This class of mixed-integer optimization models appears frequently…
Implicit-depth models such as Deep Equilibrium Networks have recently been shown to match or exceed the performance of traditional deep networks while being much more memory efficient. However, these models suffer from unstable convergence…
A Mathematical Program with Equilibrium Constraints (MPEC) is formulated to capture the relationships between multiple Mobility Service Providers (MSPs) and the users of a multi-modal transport network. The network supply structure is…
This paper presents a mathematical model for the routing of multicommodity freight in an intermodal network under disruptions. A stochastic mixed-integer program was formulated to minimize not only operational costs of various modes and…
When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in the speed at which the LP can be solved, as it is linear in the number of constraints and variables. The…
The network pricing problem (NPP) is a bilevel problem, where the leader optimizes its revenue by deciding on the prices of certain arcs in a graph, while expecting the followers (also known as the commodities) to choose a shortest path…
In this paper, we extend and improve the production chain model introduced by Kikuchi et al. (2018). Utilizing the theory of monotone concave operators, we prove the existence, uniqueness, and global stability of equilibrium price, hence…
Comparative analyses of graph structured datasets underly diverse problems. Examples of these problems include identification of conserved functional components (biochemical interactions) across species, structural similarity of large…
We investigate a modular convex Nash equilibrium problem involving nonsmooth functions acting on linear mixtures of strategies, as well as smooth coupling functions. An asynchronous block-iterative decomposition method is proposed to solve…
When stochastic control problems do not possess separability and/or monotonicity, the dynamic programming pioneered by Bellman in 1950s fails to work as a time-decomposition solution method. Such cases have posted a great challenge to the…
Decomposition methods have been proposed to approximate solutions to large sequential decision making problems. In contexts where an agent interacts with multiple entities, utility decomposition can be used to separate the global objective…
We propose a model of incentives for data pricing in large mobile networks, in which an operator wishes to balance the number of connections (active users) of different classes of users in the different cells and at different time instants,…
Multiple equilibrium states arise in many physical systems, including various types of liquid crystal structures. Having the ability to reliably compute such states enables more accurate physical analysis and understanding of experimental…
This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…
A multi-modal multi-objective optimization problem is a special kind of multi-objective optimization problem with multiple Pareto subsets. In this paper, we propose an efficient multi-modal multi-objective optimization algorithm based on…
We consider Newton methods for common types of single commodity and multi-commodity network flow problems. Despite the potentially very large dimension of the problem, they can be implemented using the conjugate gradient method and…
The decomposition or approximation of a linear operator on a matrix space as a sum of Kronecker products plays an important role in matrix equations and low-rank modeling. The approximation problem in Frobenius norm admits a well-known…
We introduce a framework based on Rockafellar's perturbation theory to analyze and solve general nonsmooth convex minimization and monotone inclusion problems involving nonlinearly composed functions as well as linear compositions. Such…