Data-Driven Patient Scheduling in Emergency Departments: A Hybrid Robust-Stochastic Approach

Emergency care necessitates adequate and timely treatment, which has unfortunately been compromised by crowding in many emergency departments (EDs). To address this issue, we study patient scheduling in EDs so that mandatory targets imposed on each patient’s door-to-provider time and length of stay can be collectively met with the largest probability. Exploiting patient flow data … Read more

Generalized Conjugate Gradient Methods for $\ell_1$ Regularized Convex Quadratic Programming with Finite Convergence

The conjugate gradient (CG) method is an efficient iterative method for solving large-scale strongly convex quadratic programming (QP). In this paper we propose some generalized CG (GCG) methods for solving the $\ell_1$-regularized (possibly not strongly) convex QP that terminate at an optimal solution in a finite number of iterations. At each iteration, our methods first … Read more

Sparse Recovery via Partial Regularization: Models, Theory and Algorithms

In the context of sparse recovery, it is known that most of existing regularizers such as $\ell_1$ suffer from some bias incurred by some leading entries (in magnitude) of the associated vector. To neutralize this bias, we propose a class of models with partial regularizers for recovering a sparse solution of a linear system. We … Read more

Acceleration of the PDHGM on strongly convex subspaces

We propose several variants of the primal-dual method due to Chambolle and Pock. Without requiring full strong convexity of the objective functions, our methods are accelerated on subspaces with strong convexity. This yields mixed rates, $O(1/N^2)$ with respect to initialisation and $O(1/N)$ with respect to the dual sequence, and the residual part of the primal … Read more

Bilevel mixed-integer linear programs and the zero forcing set

We study a class of bilevel binary linear programs with lower level variables in the upper-level constraints. Under certain assumptions, we prove that the problem can be reformulated as a single-level binary linear program, and propose a finitely terminating cut generation algorithm to solve it. We then relax the assumptions by means of a general … Read more

A Computational Comparison of Symmetry Handling Methods for Mixed Integer Programs

The handling of symmetries in mixed integer programs in order to speed up the solution process of branch-and-cut solvers has recently received significant attention, both in theory and practice. This paper compares different methods for handling symmetries using a common implementation framework. We start by investigating the computation of symmetries and analyze the symmetries present … Read more

The Strength of Dantzig-Wolfe Reformulations for the Stable Set and Related Problems

Dantzig-Wolfe reformulation of an integer program convexifies a subset of the constraints, which yields an extended formulation with a potentially stronger linear programming (LP) relaxation. We would like to better understand the strength of such reformulations in general. As a first step we investigate the classical edge formulation for the stable set problem. We characterize … Read more

Decomposition for adjustable robust linear optimization subject to uncertainty polytope

We present in this paper a general decomposition framework to solve exactly adjustable robust linear optimization problems subject to poly- tope uncertainty. Our approach is based on replacing the polytope by the set of its extreme points and generating the extreme points on the fly within row gen- eration or column-and-row generation algorithms. The novelty … Read more

Improved worst-case evaluation complexity for potentially rank-deficient nonlinear least-Euclidean-norm problems using higher-order regularized models

We present an improved evaluation complexity bound for nonlinear least squares problems using higher order regularization methods. Citation Technical Report NA 15-17, Numerical Analysis Group, University of Oxford, 2015 Article Download View Improved worst-case evaluation complexity for potentially rank-deficient nonlinear least-Euclidean-norm problems using higher-order regularized models

Blessing of Massive Scale: Spatial Graphical Model Estimation with a Total Cardinality Constraint

We consider the problem of estimating high dimensional spatial graphical models with a total cardinality constraint (i.e., the l0-constraint). Though this problem is highly nonconvex, we show that its primal-dual gap diminishes linearly with the dimensionality and provide a convex geometry justification of this ‘blessing of massive scale’ phenomenon. Motivated by this result, we propose … Read more