An Inexact General Descent Method with Applications in Differential Equation-Constrained Optimization

  • Humberto Gimenes Macedo
  • Luís Felipe Bueno
    • Categories Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    In many applications, gradient evaluations are inherently approximate, motivating the development of optimization methods that remain reliable under inexact first-order information. A common strategy in this context is adaptive evaluation, whereby coarse gradients are used in early iterations and refined near a minimizer. This is particularly relevant in differential equation–constrained optimization (DECO), where discrete adjoint … Read more

    Effective Solution Algorithms for Bulk-Robust Optimization Problems

  • Christoph Buchheim
  • Enrico Malaguti
  • Michele Monaci
  • Paolo Paronuzzi
  • Pia Schreynemackers
    • Categories 0-1 Programming, Network Optimization, Robust Optimization Tags , , , ,

    Bulk-robust optimization is a recent paradigm for addressing problems in which the structure of a system is affected by uncertainty. It considers the case in which a finite and discrete set of possible failure scenarios is known in advance, and the decision maker aims to activate a subset of available resources of minimum cost so … Read more

    A Simple First-Order Algorithm for Full-Rank Equality Constrained Optimization

  • Serge Gratton
  • Philippe L. Toint
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonlinear Systems and Least-Squares Tags , , , ,

    A very simple first-order algorithm is proposed for solving nonlinear optimization problems with deterministic nonlinear equality constraints. This algorithm adaptively selects steps in the plane tangent to the constraints or steps that reduce infeasibility, without using a merit function or a filter. The tangent steps are based on the AdaGrad method for unconstrained minimization. The … Read more

    The Branch-and-Bound Tree Closure

  • Marius Roland
  • Nagisa Sugishita
  • Alexandre Forel
  • Youssouf Emine
  • Ricardo Fukasawa
  • Thibaut Vidal
    • Categories (Mixed) Integer Linear Programming, 0-1 Programming, Cutting Plane Approaches Tags , ,

    This paper investigates the a-posteriori analysis of Branch-and-Bound (BB) trees to extract structural information about the feasible region of mixed-binary linear programs. We introduce three novel outer approximations of the feasible region, systematically constructed from a BB tree. These are: a tight formulation based on disjunctive programming, a branching-based formulation derived from the tree’s branching … Read more

    Optimization in Theory and Practice

  • Stephen Wright
    • Categories Convex Optimization, Linear Programming, Unconstrained Optimization Tags , ,

    Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their theoretical properties, optimization algorithms are interesting also for their practical usefulness as computational tools for solving real-world problems. There are often … Read more

    The Surprising Performance of Random Partial Benders Decomposition

  • Jean Pauphilet
  • Yupeng Wu
    • Categories (Mixed) Integer Linear Programming, Integer Programming, Stochastic Programming Tags ,

    Benders decomposition is a technique to solve large-scale mixed-integer optimization problems by decomposing them into a pure-integer master problem and a continuous separation subproblem. To accelerate convergence, we propose Random Partial Benders Decomposition (RPBD), a decomposition method that randomly retains a subset of the continuous variables within the master problem. Unlike existing problem-specific approaches, RPBD … Read more

    Discovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling

  • I. Esra Buyuktahtakin Toy
    • Categories (Mixed) Integer Linear Programming, Combinatorial Optimization, Meta Heuristics Tags , , , , , , ,

    TitleDiscovering Heuristics with Large Language Models (LLMs) for Mixed-Integer Programs: Single-Machine Scheduling Authorsİbrahim Oğuz Çetinkaya^1; İ. Esra Büyüktahtakın^1*; Parshin Shojaee^2; Chandan K. Reddy^2 Affiliations^1 Grado Department of Industrial and Systems Engineering, Virginia Tech, Blacksburg, VA, USA^2 Department of Computer Science, Virginia Tech, Arlington, VA, USA Abstract: Our study contributes to the scheduling and combinatorial optimization … Read more

    Optimizing Expeditionary Logistics: Dynamic Discretization for Fleet Management

  • Haden Boone
  • Mathieu Dahan
    • Categories (Mixed) Integer Linear Programming, Network Optimization, Production and Logistics Tags , , ,

    We introduce the Expeditionary Logistics Network Design Problem (ELNDP), a new formulation for operational-level planning in expeditionary environments where multi-modal vehicle coordination is critical and penalties for unmet demand dominate transportation costs. ELNDP extends the classical Scheduled Service Network Design Problem by incorporating flexible commodity sourcing and heterogeneous vehicle capabilities, both essential in military logistics. … Read more