Long wait times for elective surgery are a persistent challenge in publicly funded health systems, where hospitals must coordinate limited capacity before, during, and after the operation under considerable uncertainty. We study how a network of collaborating hospitals, such as the University Health Network in the City of Toronto, can centralize intake and jointly schedule … Read more
Augmented Lagrangian (AL) methods are a classical framework for constrained optimization, but for directly verifiable approximate KKT points, known first-order complexity bounds for standard inexact AL methods are suboptimal, while the best known proximal augmented Lagrangian (PAL) bounds retain an additional logarithmic factor. We consider linearly constrained convex composite problems with a smooth convex term … Read more
We consider a broad class of bilevel linear programs in which the follower’s decisions are all continuous, while the leader’s decisions may include integrality restrictions. Solving such problems to optimality is known to be NP-hard. A classical approach in bilevel optimization for constructing lower and upper bounds is based on a single-level relaxation, in which … Read more
We present an algorithm that finds an epsilon-approximate solution to a mixed integer quadratic programming (MIQP) problem, and that runs on a Turing machine in time polynomial in the size of the instance and in 1/epsilon, provided that the number of integer variables and the number of negative eigenvalues of the Hessian of the objective … Read more
We consider mixed-integer convex optimization problems in which binary indicators control continuous variables. We introduce the Coordinate Optimality Reformulation (CORe) framework, which augments standard indicator formulations by incorporating coordinate-wise optimality information. The resulting reformulations preserve global optimality while substantially improving branch-and-bound performance, particularly in sparse and structured settings where the coordinate-wise optimality conditions expose exploitable … Read more
We propose a single-level reformulation (SLR) for pessimistic bilevel optimization that does not rely on complementarity conditions or optimal value functions. For this reason, we refer to it as a true single-level reformulation (tSLR). A remarkable consequence is that this formulation can satisfy the classical linear independence constraint qualification, despite the fact that even the … Read more
We address the problem of optimal route planning for competitive orien- teering on real terrain. A Geographic Information System (GIS) pipeline transforms orienteering map data and digital terrain models into a fully asymmetric cost matrix that captures directional slope costs (via the Minetti metabolic model) and cumulative athlete fatigue. The resulting problem, the Asymmetric Orienteering … Read more
We consider the design of optimal fixed-step first-order methods for $M$-Lipschitz convex optimization given $\|x_0-x_\star\|\leq D$. Prior works have identified several distinct fixed-step methods, parameterized by a matrix of stepsizes $W$, with the (information-theoretic) minimax optimal rate $MD/\sqrt{N+1}$ of objective gap convergence. We provide a complete characterization of every optimal fixed-step method. Moreover, we show … Read more
Live reoptimization of operating room schedules is required to cope with disruptions such as emergency arrivals and deviations in surgery durations under strict time limits. The resulting problem can be formulated as a large-scale Resource Constrained Project Scheduling Problem (RCPSP). While exact optimization methods are attractive in this context due to their ability to provide … Read more
We study cutting-plane generation for binary polynomial optimization (BPO), whose feasible region is the multilinear set of a hypergraph. Strong inequalities for this set—such as two-links, flowers, and odd $\beta$-cycles—are classically hand-derived for fixed support patterns. Instead, we propose a decision-diagram (DD) approach: for any chosen support, it separates a facet-defining cut in the local … Read more