Month: June 2021

Dealing with inequality constraints in large-scale semidefinite relaxations for graph coloring and maximum clique problems

  • Federico Battista
  • Marianna De Santis
    • Categories Combinatorial Optimization, Convex Optimization, Semi-definite Programming Tags , ,

    Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods. However, when the dimension of the problem gets large, interior point methods become impractical in terms of both computational time and memory requirements. Certain first-order methods, such as Alternating Direction Methods of Multipliers (ADMMs), established as suitable algorithms to deal with large-scale … Read more

    A stochastic first-order trust-region method with inexact restoration for finite-sum minimization

  • Stefania Bellavia
  • Nataša Krejić
  • Benedetta Morini
  • Simone Rebegoldi
    • Categories Nonlinear Optimization Tags , , , ,

    We propose a stochastic first-order trust-region method with inexact function and gradient evaluations for solving finite-sum minimization problems. At each iteration, the function and the gradient are approximated by sampling. The sample size in gradient approximations is smaller than the sample size in function approximations and the latter is determined using a deterministic rule inspired … Read more

    The Graphical Traveling Salesperson Problem has no Integer Programming Formulation in the Original Space

  • Matthias Walter
    • Categories (Mixed) Integer Linear Programming, Graphs and Matroids

    The Graphical Traveling Salesperson Problem (GTSP) is the problem of assigning, for a given weighted graph, a nonnegative number x_e to each edge e such that the induced multi-subgraph is of minimum weight among those that are spanning, connected and Eulerian. Naturally, known mixed-integer programming formulations use integer variables x_e in addition to others. Denis … Read more

    Frank-Wolfe and friends: a journey into projection-free first-order optimization methods

  • Immanuel M. Bomze
  • Francesco Rinaldi
  • Damiano Zeffiro
    • Categories Convex Optimization, Nonlinear Optimization Tags , , , ,

    Invented some 65 years ago in a seminal paper by Marguerite Straus-Frank and Philip Wolfe, the Frank-Wolfe method recently enjoys a remarkable revival, fuelled by the need of fast and reliable first-order optimization methods in Data Science and other relevant application areas. This review tries to explain the success of this approach by illustrating versatility … Read more

    Robust Epidemiological Prediction and Optimization

  • Chenyi Fu
  • Melvyn Sim
  • Minglong Zhou
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , ,

    The COVID-19 pandemic has brought many countries to their knees, and the urgency to return to normalcy has never been greater. Epidemiological models, such as the SEIR compartmental model, are indispensable tools for, among other things, predicting how pandemic may spread over time and how vaccinations and different public health interventions could affect the outcome. … Read more

    On the Formulation Dependence of Convex Hull Pricing

  • Eugene Litvinov
  • Dane Schiro
  • Feng Zhao
  • Jinye Zhao
  • Tongxin Zheng
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Convex hull pricing provides a potential solution for reducing out-of-market payments in wholesale electricity markets. This paper revisits the theoretical construct of convex hull pricing and explores its important but underappreciated formulation-dependence property. Namely, convex hull prices may change for different formulations of the same unit commitment problem. After a conceptual exposition of the property, … Read more

    New Valid Inequalities and Formulation for the Static Chance-constrained Lot-Sizing Problem

  • Chuanhou Gao
  • James R. Luedtke
  • Zeyang Zhang
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming Tags , ,

    We study the static chance-constrained lot sizing problem, in which production decisions over a planning horizon are made before knowing random future demands, and the backlog and inventory variables are then determined by the demand realizations. The chance constraint imposes a service level constraint requiring that the probability that any backlogging is required should be … Read more

    Cardinality Minimization, Constraints, and Regularization: A Survey

  • Daniel Bienstock
  • Andrea Lodi
  • Andreas M. Tillmann
  • Alexandra Schwartz
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Constrained Nonlinear Optimization Tags , , , , , , ,

    We survey optimization problems that involve the cardinality of variable vectors in constraints or the objective function. We provide a unified viewpoint on the general problem classes and models, and give concrete examples from diverse application fields such as signal and image processing, portfolio selection, or machine learning. The paper discusses general-purpose modeling techniques and … Read more

    Escaping strict saddle points of the Moreau envelope in nonsmooth optimization

  • Damek Davis
  • Mateo Díaz
  • Dmitriy Drusvyatskiy
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    Recent work has shown that stochastically perturbed gradient methods can efficiently escape strict saddle points of smooth functions. We extend this body of work to nonsmooth optimization, by analyzing an inexact analogue of a stochastically perturbed gradient method applied to the Moreau envelope. The main conclusion is that a variety of algorithms for nonsmooth optimization … Read more

    Alternative Regularizations for OA Algorithms for Convex MINLP

  • David E. Bernal Neira
  • Ignacio E. Grossmann
  • Jan Kronqvist
  • Zedong Peng
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Nonsmooth Optimization

    In this work, we extend the regularization framework from Kronqvist et al. (https://doi.org/10.1007/s10107-018-1356-3) by incorporating several new regularization functions and develop a regularized single-tree search method for solving convex mixed-integer nonlinear programming (MINLP) problems. We propose a set of regularization functions based on distance-metrics and Lagrangean approximations, used in the projection problem for finding new … Read more