Year: 2021

Polyhedral Analysis of a Polytope from a Service Center Location Problem with a Special Decision-Dependent Customer Demand

  • Fengqiao Luo
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Polyhedra Tags , , ,

    This paper establishes and analyzes a service center location model with a simple but novel decision-dependent demand induced from a maximum attraction principle. The model formulations are investigated in the distributionally-robust optimization framework for the capacitated and uncapacitated cases. A statistical model that is based on the maximum attraction principle for estimating customer demand and … Read more

    A framework for convex-constrained monotone nonlinear equations and its special cases

  • Max L. N. Gonçalves
  • Tiago Menezes
    • Categories Nonlinear Systems and Least-Squares

    This work refers to methods for solving convex-constrained monotone nonlinear equations. We first propose a framework, which is obtained by combining a safeguard strategy on the search directions with a notion of approximate projections. The global convergence of the framework is established under appropriate assumptions and some examples of methods which fall into this framework … Read more

    A study of Liu-Storey conjugate gradient methods for vector optimization

  • Max L. N. Gonçalves
  • Leandro Fonseca Prudente
  • F. S. Lima
    • Categories Multi-Criteria Optimization, Unconstrained Optimization Tags , , ,

    This work presents a study of Liu-Storey (LS) nonlinear conjugate gradient (CG) methods to solve vector optimization problems. Three variants of the LS-CG method originally designed to solve single-objective problems are extended to the vector setting. The first algorithm restricts the LS conjugate parameter to be nonnegative and use a sufficiently accurate line search satisfying … Read more

    High-Rank Matrix Completion by Integer Programming

  • Jeff Linderoth
  • James R. Luedtke
  • Daniel Pimentel-Alarcon
  • Akhilesh Soni
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences

    In the High-Rank Matrix Completion (HRMC) problem, we are given a collection of n data points, arranged into columns of a matrix X, and each of the data points is observed only on a subset of its coordinates. The data points are assumed to be concentrated near a union of low-dimensional subspaces. The goal of … Read more

    Completely Positive Factorization by a Riemannian Smoothing Method

  • Zhijian Lai
  • Akiko Yoshise
    • Categories Linear, Cone and Semidefinite Programming Tags , , , ,

    Copositive optimization is a special case of convex conic programming, and it optimizes a linear function over the cone of all completely positive matrices under linear constraints. Copositive optimization provides powerful relaxations of NP-hard quadratic problems or combinatorial problems, but there are still many open problems regarding copositive or completely positive matrices. In this paper, … Read more

    Integrated Vehicle Routing and Service Scheduling under Time and Cancellation Uncertainties with Application in Non-Emergency Medical Transportation

  • Siqian Shen
  • Huizhu Wang
  • Xian Yu
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences

    In this paper, we consider an integrated vehicle routing and service scheduling problem for serving customers in distributed locations who need pick-up, drop-off or delivery services. We take into account the random trip time, non-negligible service time and possible customer cancellations, under which an ill-designed schedule may lead to undesirable vehicle idleness and customer waiting. … Read more

    Solving the Home Service Assignment, Routing, and Appointment Scheduling (H-SARA) problem with Uncertainties

  • Syu-Ning Johnn
  • Yiran Zhu
  • Andrés Miniguano-Trujillo
  • Akshay Gupte
    • Categories (Mixed) Integer Linear Programming, Stochastic Programming, Transportation Tags , , , ,

    The Home Service Assignment, Routing, and Appointment scheduling (H-SARA) problem integrates the strategical fleet-sizing, tactical assignment, operational vehicle routing and scheduling subproblems at different decision levels, with a single period planning horizon and uncertainty (stochasticity) from the service duration, travel time, and customer cancellation rate. We propose a two-stage stochastic mixed-integer linear programming model for … Read more

    Rank computation in Euclidean Jordan algebras

  • Michael Orlitzky
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , , ,

    Euclidean Jordan algebras are the abstract foundation for symmetriccone optimization. Every element in a Euclidean Jordan algebra has a complete spectral decomposition analogous to the spectral decomposition of a real symmetric matrix into rank-one projections. The spectral decomposition in a Euclidean Jordan algebra stems from the likewise-analogous characteristic polynomial of its elements, whose degree is … Read more

    An Efficient Retraction Mapping for the Symplectic Stiefel Manifold

  • Rafael Herrera
  • Harry Oviedo
    • Categories Constrained Nonlinear Optimization Tags , , ,

    This article introduces a new retraction on the symplectic Stiefel manifold. The operation that requires the highest computational cost to compute the novel retraction is a matrix inversion of size $2p$–by–$2p$, which is much less expensive than those required for the available retractions in the literature. Later, with the new retraction, we design a constraint … Read more

    A Fixed Point Approach with a New Solution Concept for Set-valued Optimization

  • Shengjie Li
  • Christiane Tammer
  • Chaoli Yao
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization

    We present a fixed point approach to find the whole solution set of a set-valued optimization problem though a parametric problem, in which the height of the level set of the objective function is regarded as the parameter. First, the solution concept based on the vector approach is considered in this method. Then, we propose … Read more