Month: March 2020

A Classifier to Decide on the Linearization of Mixed-Integer Quadratic Problems in CPLEX

  • Pierre Bonami
  • Andrea Lodi
  • Giulia Zarpellon
    • Categories (Mixed) Integer Linear Programming, Integer Programming, Optimization Software Design Principles Tags , , ,

    We translate the algorithmic question of whether to linearize convex Mixed-Integer Quadratic Programming problems (MIQPs) into a classification task, and use machine learning (ML) techniques to tackle it. We represent MIQPs and the linearization decision by careful target and feature engineering. Computational experiments and evaluation metrics are designed to further incorporate the optimization knowledge in … Read more

    Distribution-free Algorithms for Learning Enabled Optimization with Non-parametric Estimation

  • Shuotao Diao
  • Suvrajeet Sen
    • Categories Stochastic Programming Tags , , , ,

    This paper studies a fusion of concepts from stochastic optimization and non-parametric statistical learning, in which data is available in the form of covariates interpreted as predictors and responses. Such models are designed to impart greater agility, allowing decisions under uncertainty to adapt to the knowledge of the predictors (leading indicators). Specialized algorithms can be … Read more

    On optimality conditions for nonlinear conic programming

  • Roberto Andreani
  • Walter Gómez
  • Gabriel Haeser
  • Alberto Ramos
  • Leonardo M. Mito
    • Categories Constrained Nonlinear Optimization, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    Sequential optimality conditions have played a major role in proving stronger global convergence results of numerical algorithms for nonlinear programming. Several extensions have been described in conic contexts, where many open questions have arisen. In this paper, we present new sequential optimality conditions in the context of a general nonlinear conic framework, which explains and … Read more

    Testing Copositivity via Mixed-Integer Linear Programming

  • Kurt M. Anstreicher
    • Categories (Mixed) Integer Linear Programming, Global Optimization Theory Tags , ,

    We describe a simple method to test if a given matrix is copositive by solving a single mixed-integer linear programming (MILP) problem. This methodology requires no special coding to implement and takes advantage of the computational power of modern MILP solvers. Numerical experiments demonstrate that the method is robust and efficient. Citation Dept. of Business … Read more

    The two-echelon location-routing problem with time windows: Formulation, branch-and-price, and clustering

  • M. Saleh Farham
  • Cem Iyigun
  • Haldun Sural
    • Categories (Mixed) Integer Linear Programming, Transportation

    In this study, we consider the two-echelon location-routing problem with time windows (2E-LRPTW) to address the strategic and tactical decisions of the urban freight transportation. In the rst echelon, freights are delivered from city distribution centers (CDCs) to intermediate facilities, called satellites, in large batches. In the second echelon, goods are consolidated into smaller vehicles … Read more

    Some heuristic methods for the p-median problem with maximum distance constraints. Application to a bi-objective problem.

  • Adrián Esteban-Pérez
  • Jesús Sáez-Aguado
  • Luis A. San-José
    • Categories Facility Planning and Design, Meta Heuristics Tags , , , , ,

    In this work we study the p-median problem with maximum distance constraints (PMPDC) which is a variant of the classical p-median problem (PMP). First of all, we provide some different formulations for (PMPDC) because the heuristics procedures for the (PMPDC) with a formulation based on the approach that modifies the distance matrix that leads to … Read more

    Computing mixed strategies equilibria in presence of switching costs by the solution of nonconvex QP problems

  • Giampaolo Liuzzi
  • Marco Locatelli
  • Veronica Piccialli
  • Stefan Rass
    • Categories Game Theory, Global Optimization Applications, Quadratic Programming

    In this paper we address a game theory problem arising in the context of network security. In traditional game theory problems, given a defender and an attacker, one searches for mixed strategies which minimize a linear payoff functional. In the problem addressed in this paper an additional quadratic term is added to the minimization problem. … Read more

    Properties of the delayed weighted gradient method

  • Roberto Andreani
  • Marcos Raydan
    • Categories Unconstrained Optimization Tags , , , ,

    The delayed weighted gradient method, recently introduced in [13], is a low-cost gradient-type method that exhibits a surprisingly and perhaps unexpected fast convergence behavior that competes favorably with the well-known conjugate gradient method for the minimization of convex quadratic functions. In this work, we establish several orthogonality properties that add understanding to the practical behavior … Read more