Linearized Robust Counterparts of Two-stage Robust Optimization Problem with Applications in Operations Management

  • Amir Ardestani-Jaafari
  • Erick Delage
    • Categories Robust Optimization Tags , , ,

    In this article, we discuss an alternative method for deriving conservative approximation models for two-stage robust optimization problems. The method extends in a natural way a linearization scheme that was recently proposed to construct tractable reformulations for robust static problems involving profit functions that decompose as a sum of piecewise linear concave expressions. Given that … Read more

    Computation of Graphical Derivative for a Class of Normal Cone Mappings under a Very Weak Condition

  • Huy Chieu Nguyen
  • Le Van Hien
    • Categories Nonsmooth Optimization Tags , , , ,

    Let $\Gamma:=\{x\in \R^n\, |\, q(x)\in\Theta\},$ where $q: \R^n\rightarrow\R^m$ is a twice continuously differentiable mapping, and $\Theta$ is a nonempty polyhedral convex set in $\R^m.$ In this paper, we first establish a formula for exactly computing the graphical derivative of the normal cone mapping $N_\Gamma:\R^n\rightrightarrows\R^n,$ $x\mapsto N_\Gamma(x),$ under the condition that $M_q(x):=q(x)-\Theta$ is metrically subregular at … Read more

    A new algebraic analysis to linear mixed models

  • Yongge Tian
    • Categories Constrained Nonlinear Optimization, Statistics Tags , , , , , ,

    This article presents a new investigation to the linear mixed model $\by = \bX \bbe + \bZ\bga + \bve$ with fixed effect $\bX\bbe$ and random effect $\bZ\bga$ under a general assumption via some novel algebraic tools in matrix theory, and reveals a variety of deep and profound properties hidden behind the linear mixed model. We … Read more

    Bid Markup Decision and Resource Allocation for Cost Estimation in Competitive Bidding

  • Nobuaki Ishii
  • Yuichi Takano
  • Masaaki Muraki
    • Categories Applications - OR and Management Sciences Tags , , ,

    To receive a project contract through competitive bidding, contractors submit a bid price determined by putting a markup on the estimated project cost. Since a bid is inevitably affected by an inaccurate cost estimate, sufficient resources should be allocated to cost estimation. This paper develops a novel optimization model for determining the bid markup and … Read more

    Accelerated fast iterative shrinkage thresholding algorithms for sparsity-regularized cone-beam CT image reconstruction

  • Mark Anastasio
  • Jun Tan
  • Alex Sawatzky
  • Qiaofeng Xu
  • Deshan Yang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Optimization Software and Modeling Systems

    Purpose: The development of iterative image reconstruction algorithms for cone-beam computed tomography (CBCT) remains an active and important research area. Even with hardware acceleration, the overwhelming majority of the available 3D iterative algorithms that implement nonsmooth regularizers remain computationally burdensome and have not been translated for routine use in time-sensitive applications such as image-guided radiation … Read more

    Semi-Smooth Second-order Type Methods for Composite Convex Programs

  • Yongfeng Li
  • Zaiwen Wen
  • Xiantao Xiao
  • Liwei Zhang
    • Categories Convex Optimization Tags , , , , ,

    The goal of this paper is to study approaches to bridge the gap between first-order and second-order type methods for composite convex programs. Our key observations are: i) Many well-known operator splitting methods, such as forward-backward splitting (FBS) and Douglas-Rachford splitting (DRS), actually define a possibly semi-smooth and monotone fixed-point mapping; ii) The optimal solutions … Read more

    Statistical inference and hypotheses testing of risk averse stochastic programs

  • Vincent Guigues
  • Alexander Shapiro
  • Volker Krätschmer
    • Categories Statistics, Stochastic Programming Tags , , , , ,

    We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions when the stochastic program is expressed in terms of a law invariant coherent risk measure. The obtained results are applied … Read more

    Matroid Optimisation Problems with Nested Non-linear Monomials in the Objective Function

  • Anja Fischer
  • Frank Fischer
  • S. Thomas McCormick
    • Categories 0-1 Programming, Graphs and Matroids, Polyhedra Tags , , , , ,

    Recently, Buchheim and Klein suggested to study polynomial-time solvable optimisation problems with linear objective functions combined with exactly one additional quadratic monomial. They concentrated on special quadratic spanning tree or forest problems. We extend their results to general matroid optimisation problems with a set of nested monomials in the objective function. The monomials are linearised … Read more

    A Two-Stage Stochastic Program for Multi-shift, Multi-analyst, Workforce Optimization with Multiple On Call Options

  • Douglas S. Altner
  • Anthony C. Rojas
  • Leslie D. Servi
    • Categories Scheduling, Stochastic Programming

    Motivated by a cybersecurity workforce optimization problem, this paper investigates optimizing staffing and shift scheduling decisions given unknown demand and multiple on call staffing options at a 24/7 firm with three shifts per day, three analyst types, and several staffing and scheduling constraints. We model this problem as a two-stage stochastic program and solve it … Read more

    Nonlinear Regression Analysis by Global Optimization: A Case Study in Space Engineering

  • Alessandro Castellazzo
  • Giorgio Fasano
  • János Pintér
  • Mariachiara Vola
    • Categories Applications - Science and Engineering, Global Optimization Applications, Optimization Software and Modeling Systems Tags , , , , , ,

    The search for a better understanding of complex systems calls for quantitative model development. Within this development process, model fitting to observational data (calibration) often plays an important role. Traditionally, local optimization techniques have been applied to solve nonlinear (as well as linear) model calibration problems numerically: the limitations of such approaches in the nonlinear … Read more