Alternating active-phase algorithm for multimaterial topology optimization problems — a 115-line MATLAB implementation

  • Mohammad Mohsenie
  • Rouhollah Tavakoli
    • Categories Applications - Science and Engineering

    A new algorithm for the solution of multimaterial topology optimization problems is introduced in the present study. The presented method is based on the splitting of a multiphase topology optimization problem into a series of binary phase topology optimization sub-problems which are solved partially, in a sequential manner, using a traditional binary phase topology optimization … Read more

    Interdiction Games on Markovian PERT Networks

  • Eli Gutin
  • Daniel Kuhn
  • Wolfram Wiesemann
    • Categories Stochastic Programming Tags , , ,

    In a stochastic interdiction game a proliferator aims to minimize the expected duration of a nuclear weapons development project, while an interdictor endeavors to maximize the project duration by delaying some of the project tasks. We formulate static and dynamic versions of the interdictor’s decision problem where the interdiction plan is either pre-committed or adapts … Read more

    On the sufficiency of finite support duals in semi-infinite linear programming

  • Amitabh Basu
  • Kipp Martin
  • Christopher Thomas Ryan
    • Categories Semi-infinite Programming Tags ,

    We consider semi-infinite linear programs with countably many constraints indexed by the natural numbers. When the constraint space is the vector space of all real valued sequences, we show the finite support (Haar) dual is equivalent to the algebraic Lagrangian dual of the linear program. This settles a question left open by Anderson and Nash~\cite{anderson-nash}. … Read more

    A doubly stabilized bundle method for nonsmooth convex optimization

  • Welington de Oliveira
  • Mikhail V. Solodov
    • Categories Convex and Nonsmooth Optimization, Nonsmooth Optimization Tags , ,

    We propose a bundle method for minimizing nonsmooth convex functions that combines both the level and the proximal stabilizations. Most bundle algorithms use a cutting-plane model of the objective function to formulate a subproblem whose solution gives the next iterate. Proximal bundle methods employ the model in the objective function of the subproblem, while level … Read more

    Locally Ideal Formulations for Piecewise Linear Functions with Indicator Variables

  • Jeff Linderoth
  • James R. Luedtke
  • Srikrishna Sridhar
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering

    In this paper, we consider mixed integer linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context. CitationTechnical Report #1788, Computer Sciences Department, University of Wisconsin-Madison.ArticleDownload … Read more

    On the use of semi-closed sets and functions in convex analysis

  • Constantin Zalinescu
    • Categories Convex Optimization Tags , , , , ,

    The main aim of this short note is to show that the sub\-differentiability and duality results established by Laghdir (2005), Laghdir and Benabbou (2007), and Alimohammady \emph{et al.}\ (2011), stated in Fréchet spaces, are consequences of the corresponding known results using Moreau–Rockafellar type conditions. ArticleDownload View PDF

    Orthogonal invariance and identifiability

  • Aris Daniilidis
  • Dmitriy Drusvyatskiy
  • Adrian Lewis
    • Categories Nonsmooth Optimization Tags , , , , ,

    Orthogonally invariant functions of symmetric matrices often inherit properties from their diagonal restrictions: von Neumann’s theorem on matrix norms is an early example. We discuss the example of “identifiability”, a common property of nonsmooth functions associated with the existence of a smooth manifold of approximate critical points. Identifiability (or its synonym, “partial smoothness”) is the … Read more

    A splitting minimization method on geodesic spaces

  • João Xavier da Cruz Neto
  • Barnabé Lima
  • Pedro A. Soares Jr.
    • Categories Convex and Nonsmooth Optimization, Convex Optimization, Other Topics Tags ,

    We present in this paper the alternating minimization method on CAT(0) spaces for solving unconstraints convex optimization problems. Under the assumption that the function being minimize is convex, we prove that the sequence generated by our algorithm converges to a minimize point. The results presented in this paper are the first ones of this type … Read more

    Time (in)consistency of multistage distributionally robust inventory models with moment constraints

  • David A. Goldberg
  • Linwei Xin
    • Categories Stochastic Programming Tags , , , , , , , ,

    Recently, there has been a growing interest in developing inventory control policies which are robust to model misspecification. One approach is to posit that nature selects a worst-case distribution for any relevant stochastic primitives from some pre-specified family. Several communities have observed that a subtle phenomena known as time inconsistency can arise in this framework. … Read more