A spatial branch-and-price-and-cut algorithm for finding globally optimal solutions to the continuous network design problem

  • Michael Levin
  • David Rey
    • Categories Bilevel Optimization, Transportation Tags , , , ,

    Transportation network design, or the problem of optimizing infrastructure for a societal goal, subject to individual travelers optimizing their behavior for their own preferences arises frequently in many contexts. However, it is also an NP-hard problem due to the leader-follower or bi-level structure involving a follower objective that is different from yet significantly affects the … Read more

    A Taxonomy of Multi-Objective Alignment Techniques for Large Language Models

  • Eva Paunova
    • Categories Applications - Science and Engineering, Data Science Applications

    Aligning large language models (LLMs) with human preferences has evolved from single-objective reward maximization to sophisticated multi-objective optimization. Real-world deployment requires balancing competing objectiveshelpfulness, harmlessness, honesty, instruction-following, and task-specic capabilitiesthat often conict. This survey provides a systematic taxonomy of multi-objective alignment techniques, organizing the rapidly growing literature into four categories: (1) Reward Decomposition approaches that … Read more

    Artificial Intelligence in Supply Chain Optimization: A Systematic Review of Machine Learning Models, Methods, and Applications

  • I. Esra Buyuktahtakin Toy
    • Categories Other Topics

    Modern supply chains face mounting uncertainty and scale, motivating the integration of Artificial Intelligence (AI) and Machine Learning (ML) with mathematical optimization to enable robust and adaptive decisions. We present a systematic review of 199 articles on tangible supply chains, categorizing how ML is used—primarily for parameter estimation and for solution generation—and proposing a taxonomy … Read more

    Constraint Decomposition for Multi-Objective Instruction-Following in Large Language Models

  • Eva Paunova
    • Categories Applications - OR and Management Sciences, Robust Optimization

    Large language models (LLMs) trained with reinforcement learning from human feed- back (RLHF) struggle with complex instructions that bundle multiple, potentially con- icting requirements. We introduce constraint decomposition, a framework that separates multi-objective instructions into orthogonal componentssemantic correctness, structural organization, format specications, and meta-level requirementsand optimizes each in- dependently before hierarchical combination. Our approach addresses … Read more

    Data-Dependent Complexity of First-Order Methods for Binary Classification

  • Matthew Hough
  • Stephen A. Vavasis
    • Categories Convex Optimization, Optimization in Data Science Tags , , ,

    Large-scale problems in data science are often modeled with optimization, and the optimization model is usually solved with first-order methods that may converge at a sublinear rate. Therefore, it is of interest to terminate the optimization algorithm as soon as the underlying data science task is accomplished. We consider FISTA for solving two binary classification … Read more

    A Dual Riemannian ADMM Algorithm for Low-Rank SDPs with Unit Diagonal

  • Jie Wang
    • Categories 0-1 Programming, Semi-definite Programming Tags , , , , , , ,

    This paper proposes a dual Riemannian alternating direction method of multipliers (ADMM) for solving low-rank semidefinite programs with unit diagonal constraints. We recast the ADMM subproblem as a Riemannian optimization problem over the oblique manifold by performing the Burer-Monteiro factorization. Global convergence of the algorithm is established assuming that the subproblem is solved to certain … Read more

    A Theoretical Framework for Auxiliary-Loss-Free Load Balancing of Sparse Mixture-of-Experts in Large-Scale AI Models

  • X.Y. Han
  • Yuan Zhong
    • Categories Convex and Nonsmooth Optimization, Optimization in Data Science, Stochastic Programming Tags , , , , , , ,

    In large-scale AI training, Sparse Mixture-of-Experts (s-MoE) layers enable scaling by activating only a small subset of experts per token. An operational challenge in this design is load balancing: routing tokens to minimize the number of idle experts, which is important for the efficient utilization of (costly) GPUs. We provide a theoretical framework for analyzing … Read more

    Semidefinite programming via Projective Cutting Planes for dense (easily-feasible) instances

  • Daniel Porumbel
    • Categories Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , ,

    The cone of positive semi-definite (SDP) matrices can be described by an infinite number of linear constraints. It is well-known that one can optimize over such a feasible area by standard Cutting Planes, but work on this idea remains a rare sight, likely due to its limited practical appeal compared to Interior Point Methods (IPMs). … Read more

    Sparse Multiple Kernel Learning: Alternating Best Response and Semidefinite Relaxations

  • Dimitris Bertsimas
  • Caio de Próspero Iglesias
  • Nicholas A. G. Johnson
    • Categories Convex Optimization, Semi-definite Programming, Statistics Tags , , , ,

    We study Sparse Multiple Kernel Learning (SMKL), which is the problem of selecting a sparse convex combination of prespecified kernels for support vector binary classification. Unlike prevailing \(\ell_1\)‐regularized approaches that approximate a sparsifying penalty, we formulate the problem by imposing an explicit cardinality constraint on the kernel weights and add an \(\ell_2\) penalty for robustness. … Read more

    Subgame Perfect Methods in Nonsmooth Convex Optimization

  • Benjamin Grimmer
  • Alex L. Wang
    • Categories Convex Optimization, Nonsmooth Optimization

    This paper considers nonsmooth convex optimization with either a subgradient or proximal operator oracle. In both settings, we identify algorithms that achieve the recently introduced game-theoretic optimality notion for algorithms known as subgame perfection. Subgame perfect algorithms meet a more stringent requirement than just minimax optimality. Not only must they provide optimal uniform guarantees on … Read more