Recognizing the strength of parametric optimization to model uncertainty, we extend the classical linear programming duality theory to a parametric setting. For linear programs with parameters in general locations, we prove parametric weak and strong duality theorems and parametric complementary slackness theorems. ArticleDownload
Given a set of train routes with route costs and a set of compatible route pairs with pairing costs, the Train Single-Routing Selection Problem (TSRSP) seeks to assign one route to each train, minimizing the total cost while ensuring pairwise compatibility among the selected routes. This problem is of significant practical relevance in rail traffic … Read more
We present the architecture and central parts of the FICO Xpress Global optimization solver. In particular, we focus on how we built a global solver for the general class of mixed-integer nonlinear optimization problems by combining and extending two existing components of the FICO Xpress Solver, namely the mixed-integer linear optimization solver and the successive … Read more
This study addresses the problem of minimizing the weighted completion time variance (WCTV) in single-machine scheduling. Unlike the unweighted version, which has been extensively studied, the weighted variant introduces unique challenges due to the absence of theoretical properties that could guide the design of efficient algorithms. We propose a mathematical programming framework based on a … Read more
Collection point networks are rapidly expanding as delivery companies and public authorities promote their implementation to consolidate deliveries and reduce urban congestion. However, rather than catering to public interest by maximizing accessibility, the placement of collection points remains primarily driven by competition among delivery companies, which seek to maximize their market share. This paper thus … Read more
We present MultiObjectiveAlgorithms.jl, an open-source Julia library for solving multi-objective optimization problems written in JuMP. MultiObjectiveAlgorithms.jl implements a number of different solution algorithms, which all rely on an iterative scalarization of the problem from a multi-objective optimization problem to a sequence of single-objective subproblems. As part of this work, we extended JuMP to support vector-valued … Read more
We study the emergence of indistinguishable, but structurally distinct, allocation outcomes in convex resource allocation models. Such outcomes occur when different users receive proportionally identical allocations despite differences in initial conditions, eligibility sets, or priority weights. We formalize this behavior and analyze the structural conditions under which it arises, with a focus on fairness-oriented objectives. … Read more
We consider a game-theoretic variant of maximizing a monotone increasing, submodular function under a cardinality constraint. Initially, a solution to this classical problem is determined. Subsequently, a predetermined number of elements from the ground set, not necessarily contained in the initial solution, are deleted, potentially reducing the solution’s cardinality. If any deleted elements were part … Read more
As inherently transparent models, classification trees play a central role in interpretable machine learning by providing easily traceable decision paths that allow users to understand how input features contribute to specific predictions. In this work, we introduce a new class of interpretable binary classification models, named Pareto-optimal trees, which aim at combining the complementary strengths … Read more
This work investigates global convergence properties of a safeguarded augmented Lagrangian method applied to nonlinear programming problems, with an emphasis on the role of constraint qualifications in ensuring boundedness of the Lagrange multiplier estimates, also known as dual sequences. When functions with locally Lipschitz continuous derivatives define the constraint set, we prove that the Error … Read more