Machine Learning–Enhanced Column Generation for Large-Scale Capacity Planning Problems

  • Felipe Keim
  • Victor Bucarey
  • Qi Zhang
  • Angela Flores-Quiroz
    • Categories (Mixed) Integer Linear Programming, Energy, Facility Planning and Design Tags , ,

    Capacity Planning problems are a class of optimization problems used in diverse industries to improve resource allocation and make investment decisions. Solving real-world instances of these problems typically requires significant computational effort. To tackle this, we propose machine-learning-aided column generation methods for solving large-scale capacity planning problems. Our goal is to accelerate column generation by … Read more

    AI for Enhancing Operations Research of Agriculture and Energy

  • Morteza Kimiaei
  • Anshu Kumar
  • Vyacheslav Kungurtsev
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Global Optimization Tags , , , , , , ,

    This paper surveys optimization problems arising in agriculture, energy systems, and water-energy coordination from an operations research perspective. These problems are commonly formulated as integer nonlinear programs, mixed-integer nonlinear programs, or combinatorial set optimization models, characterized by nonlinear physical constraints, discrete decisions, and intertemporal coupling. Such structures pose significant computational challenges in large-scale and repeated-solution … Read more

    New Location Science Models with Applications to UAV-Based Disaster Relief

  • Sina Kazemdehbashi
  • Boris S. Mordukhovich
  • Yanchao Liu
    • Categories Convex and Nonsmooth Optimization, Facility Planning and Design Tags , , , ,

    Natural and human-made disasters can cause severe devastation and claim thousands of lives worldwide. Therefore, developing efficient methods for disaster response and management is a critical task for relief teams. One of the most essential components of effective response is the rapid collection of information about affected areas, damages, and victims. More data translates into … Read more

    Solving Stengle’s Example in Rational Arithmetic: Exact Values of the Moment-SOS Relaxations

  • Didier Henrion
    • Categories Semi-definite Programming Tags , , , ,

    We revisit Stengle’s classical univariate polynomial optimization example $\min 1-x^2$ s.t. $(1-x^2)^3\ge 0$ whose constraint description is degenerate at the minimizers. We prove that the moment-SOS hierarchy of relaxation order $r\ge 3$ has the exact value $-1/r(r-2)$. For this we construct in rational arithmetic a dual polynomial sum-of-squares (SOS) certificate and a primal moment sequence … Read more

    A Proximal-Gradient Method for Solving Regularized Optimization Problems with General Constraints

  • Daniel P. Robinson
  • Frank E. Curtis
  • Xiaoyi Qu
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

    We propose, analyze, and test a proximal-gradient method for solving regularized optimization problems with general constraints. The method employs a decomposition strategy to compute trial steps and uses a merit function to determine step acceptance or rejection. Under various assumptions, we establish a worst-case iteration complexity result, prove that limit points are first-order KKT points, … Read more

    An active-set method for box-constrained multiobjective optimization

  • N. S. Fazzio
  • Leandro Fonseca Prudente
  • María Laura Schuverdt
    • Categories Multi-Criteria Optimization Tags , , ,

    We propose an active-set algorithm for smooth multiobjective optimization problems subject to box constraints. The method works on one face of the feasible set at a time, treating it as a lower-dimensional region on which the problem simplifies. At each iteration, the algorithm decides whether to remain on the current face or to move to … Read more

    Global optimization of low-rank polynomials

  • Llorenç Balada Gaggioli
  • Didier Henrion
  • Milan Korda
    • Categories Global Optimization, Semi-definite Programming

    This work considers polynomial optimization problems where the objective admits a low-rank canonical polyadic tensor decomposition. We introduce LRPOP (low-rank polynomial optimization), a new hierarchy of semidefinite programming relaxations for which the size of the semidefinite blocks is determined by the canonical polyadic rank rather than the number of variables. As a result, LRPOP can … Read more

    Primal-dual resampling for solution validation in convex stochastic programming

  • Yi Chu
  • Susan R. Hunter
  • Raghu Pasupathy
    • Categories Convex Optimization, Optimization in Data Science, Stochastic Programming Tags , ,

    Suppose we wish to determine the quality of a candidate solution to a convex stochastic program in which the objective function is a statistical functional parameterized by the decision variable and known deterministic constraints may be present. Inspired by stopping criteria in primal-dual and interior-point methods, we develop cancellation theorems that characterize the convergence of … Read more

    Exact and approximate formulations for the close-enough TSP

  • Domingo Araya
  • Gustavo Angulo
  • Margarita P Castro
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms Tags , ,

    This work addresses the Close-Enough Traveling Salesman Problem (CETSP), a variant of the classic traveling salesman problem in which we seek to visit neighborhoods of points in the plane (defined as disks) rather than specific points. We present two exact formulations for this problem based on second-order cone programming (SOCP), along with approximated mixed-integer linear … Read more

    Facial reduction for nice (and non-nice) convex programs

  • Ying Lin
  • Tianxiang Liu
  • Bruno F. Lourenço
    • Categories Convex and Nonsmooth Optimization, Convex Optimization Tags , , ,

    Consider the primal problem of minimizing the sum of two closed proper convex functions \(f\) and \(g\). If the relative interiors of the domains of \(f\) and \(g\) intersect, then the primal problem and its corresponding Fenchel dual satisfy strong duality. When these relative interiors fail to intersect, pathologies and numerical difficulties may occur. In … Read more