We analyze restarted PDHG on totally unimodular linear programs. In particular, we show that restarted PDHG finds an ϵ-optimal solution in O ( H m 1 2.5 nnz ( A ) log ⁡ ( H m 2 / ϵ ) ) matrix-vector multiplies where m 1 is the number of ...

We consider the problem of packing a given number of congruent circles with the maximum radius in a unit square as a mathematical optimization problem. Due to the presence of non-overlapping constraints, this problem is a notoriously difficult ...

We consider the lost-sales inventory systems with stochastic lead times and establish the asymptotic optimality of base-stock policies for such systems. Specifically, we prove that as the per-unit lost-sales penalty cost becomes large compared to ...

This paper introduces the Traveling Salesman Problem (TSP) with Backend Information Processing (bTSP), which integrates backend processing times into path planning to minimize the makespan. The study develops a mixed integer linear programming ...

We consider a lift-and-project approach for the cardinality-constrained Boolean quadric polytope. Some upper bounds for the distance between the polytope and its linear approximation are derived. Unsurprisingly, the distance converges to 0 when ...

Graphical designs are a framework for sampling and numerical integration of functions on graphs. In this note, we introduce a method to address the trade-off between graphical design sparsity and accuracy. We show how to obtain sparse graphical ...

This paper proposes pandemic mitigation vaccination policies for Newfoundland and Labrador (NL) based on two compact mixed integer programming (MIP) models of the distance-based critical node detection problem (DCNDP). Our main focus is on two ...

This paper considers one-warehouse multiple-retailer inventory systems. The retailers are non-identical and face Poisson demand processes. We consider an integer-ratio policy in which each retailer orders in a fixed interval that is either an ...

Uncertainty reduction has recently been introduced in the robust optimization literature as a relevant special case of decision-dependent uncertainty. Herein, we identify two relevant situations in which the problem is polynomially solvable. We ...

We aim at generalizing formulations for non-convex piecewise-linear problems to mathematical programs whose non-convexities are only expressed in terms of piecewise-convex univariate functions. This is motivated by solving Mixed-Integer Non-...

We study a penalty reformulation of constrained convex optimization based on the softplus penalty function. For strongly convex objectives, we develop upper bounds on the objective value gap and the violation of constraints for the solutions to ...

It is a well-known result that bilevel linear optimization is NP-hard. In many publications, reformulations as mixed-integer linear optimization problems are proposed, which suggests that the decision version of the problem belongs to NP. However,...

We consider bilevel linear programs (BLPs) that model hierarchical decision-making settings with two independent decision-makers (DMs), referred to as a leader (an upper-level DM) and a follower (a lower-level DM). BLPs are strongly NP-hard. In ...

One of the oldest results in scheduling theory is that the Shortest Processing Time (SPT) rule finds an optimal solution to the problem of scheduling jobs on identical parallel machines to minimize average job completion times. We ...

Prediction models are traditionally optimized independently from decision-based optimization. Conversely, a ‘smart predict then optimize’ (SPO) framework optimizes prediction models to minimize downstream decision regret. In this paper ...

Let us consider a network flow respecting arc capacities and flow conservation constraints. The flow degree of a node is sum of the flow entering and leaving it. We study the problem of determining a flow that minimizes the maximum ...

• Introduction of a new formulation for the minimum maximum flow degree problem.
• ...

We estimate the increase in minimum value for a decision that is robust to parameter perturbations as compared to the value of a nominal nonconvex problem. The estimates rely on expressions for subgradients and local Lipschitz moduli ...

Distributed consensus optimization has received considerable attention in recent years and several distributed consensus-based algorithms have been proposed for (nonsmooth) convex and (smooth) nonconvex objective functions. However, ...

We consider an intensity control problem for a point process to maximize the expectation of a function of the time when the nth event occurs. We find the optimal control policy when the objective function is unimodal. Moreover, if the ...

This paper presents a mixed-integer linear programming formulation for the multi-mode resource-constrained project scheduling problem with uncertain activity durations. We consider a two-stage robust optimisation approach and find solutions that ...