A specialized interior-point algorithm for huge minimum convex cost flows in bipartite networks

The computation of the Newton direction is the most time consuming step of interior-point methods. This direction was efficiently computed by a combination of Cholesky factorizations and conjugate gradients in a specialized interior-point method for block-angular structured problems. In this work we apply this algorithmic approach to solve very large instances of minimum cost flows … Read more

Multi-step discrete-time Zhang neural networks with application to time-varying nonlinear optimization

As a special kind of recurrent neural networks, Zhang neural network (ZNN) has been successfully applied to various time-variant problems solving. In this paper, we first propose a special two-step Zhang et al. discretization (ZeaD) formula and a general two-step ZeaD formula, whose truncation errors are ${O}(\tau^3)$ and ${O}(\tau^2)$, respectively, and $\tau>0$ denotes the sampling … Read more

An almost cyclic 2-coordinate descent method for singly linearly constrained problems

A block decomposition method is proposed for minimizing a (possibly non-convex) continuously differentiable function subject to one linear equality constraint and simple bounds on the variables. The proposed method iteratively selects a pair of coordinates according to an almost cyclic strategy that does not use first-order information, allowing us not to compute the whole gradient … Read more

Decomposition Methods for Solving Markov Decision Processes with Multiple Models of the Parameters

We consider the problem of decision-making in Markov decision processes (MDPs) when the reward or transition probability parameters are not known with certainty. We consider an approach in which the decision-maker (DM) considers multiple models of the parameters for an MDP and wishes to find a policy that optimizes an objective function that considers the … Read more

The Benefits of Transfers in Crowdsourced Pickup-and-Delivery Systems

Rapid urban growth, the increasing importance of e-commerce and high consumer service expectations have given rise to new and innovative models for freight delivery within urban environments. Crowdsourced solutions – where drivers are not employed by a carrier but occasionally offer their services through on-line platforms and are contracted as required by carriers – are … Read more

Robust Data-Driven Vehicle Routing with Time Windows

Optimal routing solutions based on deterministic models usually fail to deliver promised on-time services in an uncertain real world, which can lead to the loss of customers and revenue. We study a vehicle routing problem with time windows (VRPTW) toward the end of mitigating the risk of late customer arrivals as much as possible when … Read more

Parallelizing Subgradient Methods for the Lagrangian Dual in Stochastic Mixed-Integer Programming

The dual decomposition of stochastic mixed-integer programs can be solved by the projected subgradient algorithm. We show how to make this algorithm more amenable to parallelization in a master-worker model by describing two approaches, which can be combined in a natural way. The first approach partitions the scenarios into batches, and makes separate use of … Read more

The Impact of Potential-Based Physics Models on Pricing in Energy Networks

Pricing of access to energy networks is an important issue in liberalized energy sectors because of the natural monopoly character of the underlying transport infrastructures. We introduce a general pricing framework for potential-based energy flows in arbitrarily structured transport networks. In different specifications of our general pricing model we discuss first- and second-best pricing results … Read more

Basis Pursuit Denoise with Nonsmooth Constraints

Level-set optimization formulations with data-driven constraints minimize a regularization functional subject to matching observations to a given error level. These formulations are widely used, particularly for matrix completion and sparsity promotion in data interpolation and denoising. The misfit level is typically measured in the l2 norm, or other smooth metrics. In this paper, we present … Read more

Multi-component Maintenance Optimization: A Stochastic Programming Approach

Maintenance optimization has been extensively studied in the past decades. However, most of the existing maintenance models focus on single-component systems. Multi-component maintenance optimization, which joins the stochastic failure processes with the combinatorial maintenance grouping problems, remains as an open issue. To address this challenge, we study this problem in a finite planning horizon by … Read more