A Primal-Dual Frank-Wolfe Algorithm for Linear Programming

\(\) We present two first-order primal-dual algorithms for solving saddle point formulations of linear programs, namely FWLP (Frank-Wolfe Linear Programming) and FWLP-P. The former iteratively applies the Frank-Wolfe algorithm to both the primal and dual of the saddle point formulation of a standard-form LP. The latter is a modification of FWLP in which regularizing perturbations … Read more

The MIP Workshop 2023 Computational Competition on Reoptimization

This paper describes the computational challenge developed for a computational competition held in 2023 for the 20th anniversary of the Mixed Integer Programming Workshop. The topic of this competition was reoptimization, also known as warm starting, of mixed integer linear optimization problems after slight changes to the input data for a common formulation. The challenge … Read more

Adjustable robust optimization for fleet sizing problem in closed-loop supply chains with simultaneous delivery and pickup

The Fleet Sizing Problem (FSP) stands as a critical challenge within the realm of logistics and supply chain management, particularly in the context of Closed-Loop Supply Chains (CLSC). The significance of addressing the FSP lies in its direct impact on operational costs, resource utilization, and environmental sustainability. By effectively optimizing fleet size, organizations can streamline … Read more

Fourth-order Marginal Moment Model: Reformulations and Applications

This paper investigates the bounds on the expectation of combinatorial optimization given moment information for each individual random variable. A popular approach to solving this problem, known as the marginal moment model (MMM), is to reformulate it as a semidefinite program (SDP). In this paper, we investigate the structure of MMM with up to fourth-order … Read more

The SCIP Optimization Suite 9.0

The SCIP Optimization Suite provides a collection of software packages for mathematical optimization, centered around the constraint integer programming (CIP) framework SCIP. This report discusses the enhancements and extensions included in the SCIP Optimization Suite 9.0. The updates in SCIP 9.0 include improved symmetry handling, additions and improvements of nonlinear handlers and primal heuristics, a … Read more

Distributed Task Assignment in a Swarm of UAVs

We consider the problem of distributed task assignment in a swarm of Unmanned Aerial Vehicles (UAVs), where heterogeneous agents that can have different capabilities need to work in teams to execute tasks. We consider the case where communication between UAVs is costly or dangerous and should be limited or avoided, while individual UAVs have uncertain … Read more

Binary Integer Program Reformulation: A Set System Approximation Approach

This paper presents a generic reformulation framework for binary integer programs (BIPs) without imposing additional specifications for the objective function or constraints. To facilitate such generality, we introduce a set system approximation theory designed to identify the tightest inner and outer approximations for any binary solution space using special types of set systems. This development … Read more

On Averaging and Extrapolation for Gradient Descent

\(\) This work considers the effect of averaging, and more generally extrapolation, of the iterates of gradient descent in smooth convex optimization. After running the method, rather than reporting the final iterate, one can report either a convex combination of the iterates (averaging) or a generic combination of the iterates (extrapolation). For several common stepsize … Read more

On Coupling Constraints in Linear Bilevel Optimization

It is well-known that coupling constraints in linear bilevel optimization can lead to disconnected feasible sets, which is not possible without coupling constraints. However, there is no difference between linear bilevel problems with and without coupling constraints w.r.t. their complexity-theoretical hardness. In this note, we prove that, although there is a clear difference between these … Read more