We consider a nonlinear nonconvex network flow problem that arises, for example, in natural gas or water transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides … Read more
In this paper we consider a network with P nodes, where each node has exclusive access to a local cost function. Our contribution is a communication-efficient distributed algorithm that finds a vector x* minimizing the sum of all the functions. We make the additional assumption that the functions have intersecting local domains, i.e., each function … Read more
We consider a robust shortest path problem when the cost coefficient is the product of two uncertain factors. We first show that the robust problem can be solved in polynomial time by a dual variable enumeration with shortest path problems as subproblems. We also propose a path enumeration approach using a $K$-shortest paths finding algorithm … Read more
This paper presents optimal scaling of the alternating directions method of multipliers (ADMM) algorithm for a class of distributed quadratic programming problems. The scaling corresponds to the ADMM step-size and relaxation parameter, as well as the edge-weights of the underlying communication graph. We optimize these parameters to yield the smallest convergence factor of the algorithm. … Read more
In this paper, we consider relocating facilities, where we have demand changes in the network. Relocations are performed by closing some of the existing facilities from low demand areas and opening new ones in newly emerging areas. However, the actual changes of demand are not known in advance. Therefore, di erent scenarios with known probabilities are … Read more
We introduce a class of incremental network design problems focused on investigating the optimal choice and timing of network expansions. We concentrate on an incremental network design problem with shortest paths. We investigate structural properties of optimal solutions, we show that the simplest variant is NP-hard, we analyze the worst-case performance of natural greedy heuristics, … Read more
In this paper, we consider the network loading problem under demand uncertainties with static routing, i.e, a single routing scheme based on the fraction of the demands has to be determined. We generalize the class of metric inequalities to the Γ-robust setting and show that they yield a formulation in the capacity space. We describe … Read more
In this paper we present a variant of random coordinate descent method for solving linearly constrained convex optimization problems with composite objective function. If the smooth part has Lipschitz continuous gradient, then the method terminates with an ϵ-optimal solution in O(N2/ϵ) iterations, where N is the number of blocks. For the class of problems with … Read more
We examine the problem of placing stationary monitors in a continuous space, with the goal of minimizing an adversary’s maximum probability of traversing an origin-destination route without being detected. The problem arises, for instance, in defending against the transport of illicit material through some area of interest. In particular, we consider the deployment of monitors … Read more
The minimum concave cost network flow problem (MCCNFP) is NP-hard, but efficient polynomial-time algorithms exist for some special cases such as the uncapacitated lot-sizing problem and many of its variants. We study the MCCNFP over a grid network with a general nonnegative separable concave cost function. We show that this problem is polynomially solvable when … Read more