New subspace minimization conjugate gradient methods based on regularization model for unconstrained optimization

  • Hongwei Liu
  • Zhao Ting
  • Zexian Liu
    • Categories Applications - OR and Management Sciences Tags , , , ,

    In this paper, two new subspace minimization conjugate gradient methods based on p-regularization models are proposed, where a special scaled norm in p-regularization model is analyzed. Diffierent choices for special scaled norm lead to different solutions to the p-regularized subproblem. Based on the analyses of the solutions in a two-dimensional subspace, we derive new directions … Read more

    Dual Decomposition of Two-Stage Distributionally Robust Mixed-Integer Programming under the Wasserstein Ambiguity Set

  • Kibaek Kim
    • Categories (Mixed) Integer Linear Programming, Robust Optimization, Stochastic Programming Tags , ,

    We develop a dual decomposition of two-stage distributionally robust mixed-integer programming (DRMIP) under the Wasserstein ambiguity set. The dual decomposition is based on the Lagrangian dual of DRMIP, which results from the Lagrangian relaxation of the nonanticipativity constraints and min-max inequality. We present two Lagrangian dual problem formulations, each of which is based on different principle. We show … Read more

    Estimating the Size of Branch-and-Bound Trees

  • Daniel Anderson
  • Gregor Hendel
  • Pierre Le Bodic
  • Marc E. Pfetsch
    • Categories (Mixed) Integer Linear Programming

    This paper investigates the estimation of the size of Branch-and-Bound (B&B) trees for solving mixed-integer programs. We first prove that the size of the B&B tree cannot be approximated within a factor of~2 for general binary programs, unless P equals NP. Second, we review measures of the progress of the B&B search, such as the … Read more

    On monotonicity and search traversal in copositivity detection algorithms

  • Leocadio G Casado
  • Eligius M.T. Hendrix
  • Boglárka Tóth
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Quadratic Programming Tags , , ,

    Matrix copositivity has an important theoretical background. Over the last decades, the use of algorithms to check copositivity has made a big progress. Methods are based on spatial branch and bound, transformation to Mixed Integer Programming, implicit enumeration of KKT points or face-based search. Our research question focuses on exploiting the mathematical properties of the … Read more

    Generation Expansion Planning with Revenue Adequacy Constraints

  • Cheng Guo
  • Merve Bodur
  • Dimitri J. Papageorgiou
    • Categories Applications - Science and Engineering Tags , , , ,

    Generation capacity expansion models have traditionally taken the vantage point of a centralized planner seeking to find cost-optimal generation capacity to reliably meet load over decadal time scales. Often assuming perfectly competitive players, these models attempt to provide guidance for system planners without necessarily ensuring that individual generators are adequately remunerated for their generation, flexibility, … Read more

    Submodular maximization of concave utility functions composed with a set-union operator with applications to maximal covering location problems

  • Stefano Coniglio
  • Fabio Furini
  • Ivana Ljubić
    • Categories Cutting Plane Approaches, Integer Programming, Nonlinear Optimization Tags , ,

    We study a family of discrete optimization problems asking for the maximization of the expected value of a concave, strictly increasing, and differentiable function composed with a set-union operator. The expected value is computed with respect to a set of coefficients taking values from a discrete set of scenarios. The function models the utility function … Read more

    A termination criterion for stochastic gradient descent for binary classification

  • Sina Baghal
  • Courtney Paquette
  • Stephen A. Vavasis
    • Categories Convex and Nonsmooth Optimization

    We propose a new, simple, and computationally inexpensive termination test for constant step-size stochastic gradient descent (SGD) applied to binary classification on the logistic and hinge loss with homogeneous linear predictors. Our theoretical results support the effectiveness of our stopping criterion when the data is Gaussian distributed. This presence of noise allows for the possibility … Read more

    An Exact Solution Method for the TSP with Drone Based on Decomposition

  • Gustavo Angulo
  • Mathias A. Klapp
  • Sebastián A. Vásquez
    • Categories (Mixed) Integer Linear Programming, Production and Logistics Tags , , ,

    The Traveling Salesperson Problem with Drone (TSP–D) is a routing model in which a given set of customer locations must be visited in the least amount of time, either by a truck route starting and ending at a depot or by a drone dispatched from the truck en route. We study the TSP–D model and … Read more

    A Model of Supply-Chain Decisions for Resource Sharing with an Application to Ventilator Allocation to Combat COVID-19

  • Sanjay Mehrotra
  • Hamed Rahimian
  • Masoud Barah
  • Fengqiao Luo
  • Karolina Schantz
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , , ,

    We present a stochastic optimization model for allocating and sharing a critical resource in the case of a pandemic. The demand for different entities peaks at different times, and an initial inventory for a central agency is to be allocated. The entities (states) may share the critical resource with a different state under a risk-averse … Read more

    Using gradient directions to get global convergence of Newton-type methods

  • Daniela di Serafino
  • Gerardo Toraldo
  • Marco Viola
    • Categories Unconstrained Optimization

    The renewed interest in Steepest Descent (SD) methods following the work of Barzilai and Borwein [IMA Journal of Numerical Analysis, 8 (1988)] has driven us to consider a globalization strategy based on SD, which is applicable to any line-search method. In particular, we combine Newton-type directions with scaled SD steps to have suitable descent directions. … Read more