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
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
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
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
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
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
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
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
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
LSP(n), the largest small polygon with n vertices, is defined as the polygon of unit diameter that has maximal area A(n). Finding the configuration LSP(n) and the corresponding A(n) for even values n >= 6 is a long-standing challenge that leads to an interesting class of nonlinear optimization problems. We present numerical solution estimates for … Read more