An optimal control theory for accelerated optimization
Accelerated optimization algorithms can be generated using a double-integrator model for the search dynamics imbedded in an optimal control problem. CitationunpublishedArticleDownload View PDF
Risk Aversion to Parameter Uncertainty in Markov Decision Processes with an Application to Slow-Onset Disaster Relief
In classical Markov Decision Processes (MDPs), action costs and transition probabilities are assumed to be known, although an accurate estimation of these parameters is often not possible in practice. This study addresses MDPs under cost and transition probability uncertainty and aims to provide a mathematical framework to obtain policies minimizing the risk of high long-term … Read more
A Computational Comparison of Optimization Methods for the Golomb Ruler Problem
The Golomb ruler problem is defined as follows: Given a positive integer n, locate n marks on a ruler such that the distance between any two distinct pair of marks are different from each other and the total length of the ruler is minimized. The Golomb ruler problem has applications in information theory, astronomy and … Read more
A polynomial algorithm for minimizing travel time in time-dependent networks with waits
We consider a time-dependent shortest path problem with possible waiting at each node and a global bound $W$ on the total waiting time. The goal is to minimize only the time travelled along the edges of the path, not including the waiting time. We prove that the problem can be solved in polynomial time when … Read more
Optimizing the Recovery of Disrupted Multi-Echelon Assembly Supply Chain Networks
We consider optimization problems related to the scheduling of multi-echelon assembly supply chain (MEASC) networks that have applications in the recovery from large-scale disruptive events. Each manufacturer within this network assembles a component from a series of sub-components received from other manufacturers. We develop scheduling decision rules that are applied locally at each manufacturer and … Read more
Dynamic Discretization Discovery Algorithms for Time-Dependent Shortest Path Problems
Finding a shortest path in a network is an iconic optimization problem. We focus on settings in which the travel time on an arc in the network depends on the time at which traversal of the arc begins. In such settings, reaching the sink as early as possible is not the only objective of interest. … Read more
Time-Dependent Shortest Path Problems with Penalties and Limits on Waiting
Waiting at the right location at the right time can be critically important in certain variants of time-dependent shortest path problems. We investigate the computational complexity of time-dependent shortest path problems in which there is either a penalty on waiting or a limit on the total time spent waiting at a given subset of the … Read more
Pathfollowing for Parametric Mathematical Programs with Complementarity Constraints
In this paper we study procedures for pathfollowing parametric mathematical pro- grams with complementarity constraints. We present two procedures, one based on the penalty approach to solving standalone MPCCs, and one based on tracing active set bifurcations aris- ing from doubly-active complementarity constraints. We demonstrate the performance of these approaches on a variety of examples … Read more
A two-level distributed algorithm for nonconvex constrained optimization
This paper aims to develop distributed algorithms for nonconvex optimization problems with complicated constraints associated with a network. The network can be a physical one, such as an electric power network, where the constraints are nonlinear power flow equations, or an abstract one that represents constraint couplings between decision variables of different agents. Despite the … Read more
Recovery of a mixture of Gaussians by sum-of-norms clustering
Sum-of-norms clustering is a method for assigning $n$ points in $\R^d$ to $K$ clusters, $1\le K\le n$, using convex optimization. Recently, Panahi et al.\ proved that sum-of-norms clustering is guaranteed to recover a mixture of Gaussians under the restriction that the number of samples is not too large. The purpose of this note is to … Read more