An instance of the quadratic minimum spanning tree problem (QMSTP) is called linearizable if it can be rewritten as an instance of the linear minimum spanning tree problem in such a way that the objective function value is preserved at all feasible solutions. Previous work has shown that a sufficient condition for linearizability is that … Read more
This paper introduces the class of weakly quasar-convex functions, a notion that simultaneously generalizes weak convexity (and hence convexity) and quasar-convexity. We establish the theoretical foundation for this new class by developing its basic calculus, deriving characterizations, and systematically investigating its closure and structural properties. Building on these tools, we analyze the proximal point algorithm … Read more
We present GPU-accelerated Bregman Douglas–Rachford splitting algorithm (BDRS) for discrete optimal transport problem in three input formats: an explicit cost matrix, a point cloud with a ground cost between them, and a separable cost on a regular grid. For each input format, we propose hardware-aware designs of mathematically equivalent representations for the BDRS iterations to … Read more
We study robust optimization problems with decision-dependent information discovery under polyhedral uncertainty and continuous recourse. We first establish structural properties of the resulting min–max–min problem, including existence of solutions and a condition under which information discovery has no value. Then, we develop a heuristic approach that combines affine decision rules with scenario generation and show … Read more
Deep hedging learns trading policies from historical or simulated market trajectories, yet under nonstationarity these training paths may not represent future market conditions. We propose WRAP (Wasserstein-Reweighting Adversarial Perturbation), a drift-aware adversarial training framework derived from a two-budget distributionally robust optimization (DRO) formulation. The formulation is anchored to a weighted empirical reference distribution whose fixed … Read more
We study stochastic optimization with a completely unobserved target distribution and samples from related source distributions. Treating the sources and the target as independent draws from a common meta-distribution, we propose Wasserstein-metric meta-distribution support learning (MDSL). The model jointly learns the center and radius of a Wasserstein ball, with an exclusion parameter controlling the fraction … Read more
We construct small extended formulations for nonnegative integer flows whose arc labels have a prescribed sum in a finite abelian group. For circulations, the formulation is a single integral network that combines cycles even when they lie in different components. This yields an O(Δn²) bound for strictly Δ-modular cographic integer hulls of translated cones, improving … Read more
We propose a data-driven linear programming model to compute energy-optimal timetables for networks operating under communications-based train control (CBTC); the model was developed in collaboration with Hitachi Rail Canada, the largest provider of CBTC systems worldwide. Our model minimizes the network’s effective energy consumption, defined as the total traction energy consumed by the trains minus … Read more
This paper studies the single-machine problem of minimizing the weighted completion time variance (WCTV) and proposes a polynomially computable lower-bounding framework that generalizes the benchmark introduced by Nessah and Chu (2010). We first develop a generalized augmented-sequence decomposition that mathematically connects the weighted problem with the classical unweighted variance setting. Using this decomposition, we derive … Read more
Exact mathematical programming formulations for estimating classification rules provide guarantees of empirical optimality, but their size grows rapidly with the number of predictive features and model complexity. This paper shows that interpretable classifiers can be estimated by directly maximizing empirical classification accuracy under complexity constraints, using truncation and warm-start strategies compatible with disjunctive normal form … Read more