On convergence rate of the Douglas-Rachford operator splitting method
This note provides a simple proof on a O(1/k) convergence rate for the Douglas-Rachford operator splitting method where $k$ denotes the iteration counter. ArticleDownload View PDF
Optimizing the Spectral Radius
We suggest an approach for finding the maximal and the minimal spectral radius of linear operators from a given compact family of operators, which share a common invariant cone (e.g. for a family of nonnegative matrices). In case of families with so-called product structure, this leads to efficient algorithms for optimizing the spectral radius and … Read more
The Asymmetric Quadratic Traveling Salesman Problem
The quadratic traveling salesman problem asks for a tour of minimal costs where the costs are associated with each two arcs that are traversed in succession. This structure arises, e. g., if the succession of two arcs represents the costs of loading processes in transport networks or a switch between different technologies in communication networks. … Read more
DC approach to regularity of convex multifunctions with applications to infinite systems
The paper develops a new approach to the study of metric regularity and related well-posedness properties of convex set-valued mappings between general Banach spaces by reducing them to unconstrained minimization problems with objectives given as the difference of convex (DC) functions. In this way we establish new formulas for calculating the exact regularity bound of … Read more
The recoverable robust tail assignment problem
Schedule disruptions are commonplace in the airline industry with many flight-delaying events occurring each day. Recently there has been a focus on introducing robustness into airline planning stages to reduce the effect of these disruptions. We propose a recoverable robustness technique as an alternative to robust optimisation to reduce the effect of disruptions and the … Read more
Optimizing Trading Decisions for Hydro Storage Systems using Approximate Dual Dynamic Programming
We propose a new approach to optimize operations of hydro storage systems with multiple connected reservoirs which participate in wholesale electricity markets. Our formulation integrates short-term intraday with long-term interday decisions. The intraday problem considers bidding decisions as well as storage operation during the day and is formulated as a stochastic program. The interday problem … Read more
Robust and Trend-following Student’s t Kalman Smoothers
Two nonlinear Kalman smoothers are proposed using the Student’s t distribution. The first, which we call the T-Robust smoother, finds the maximum a posteriori (MAP) solution for Gaussian process noise and Student’s t observation noise. It is extremely robust against outliers, outperforming the recently proposed L1-Laplace smoother in extreme situations with data containing 20% or … Read more
A Family of Newton Methods for Nonsmooth Constrained Systems with Nonisolated Solutions
We propose a new family of Newton-type methods for the solution of constrained systems of equations. Under suitable conditions, that do not include differentiability or local uniqueness of solutions, local, quadratic convergence to a solution of the system of equations can be established. We show that as particular instances of the method we obtain inexact … Read more
A randomized Mirror-Prox method for solving structured large-scale matrix saddle-point problems
In this paper, we derive a randomized version of the Mirror-Prox method for solving some structured matrix saddle-point problems, such as the maximal eigenvalue minimization problem. Deterministic first-order schemes, such as Nesterov’s Smoothing Techniques or standard Mirror-Prox methods, require the exact computation of a matrix exponential at every iteration, limiting the size of the problems … Read more
Hedge algorithm and Dual Averaging schemes
We show that the Hedge algorithm, a method that is widely used in Machine Learning, can be interpreted as a particular instance of Dual Averaging schemes, which have recently been introduced by Nesterov for regret minimization. Based on this interpretation, we establish three alternative methods of the Hedge algorithm: one in the form of the … Read more