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

    On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem

  • Andrey Kibzun
  • Vladimir I. Norkin
  • Andrey Naumov
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , ,

    We suggest a method for equivalent transformation of a quantile optimization problem with discrete distribution of random parameters to mixed integer programming problems. The number of additional integer (in fact boolean) variables in the equivalent problems equals to the number of possible scenarios for random data. The obtained mixed integer problems are solved by standard … Read more

    Properly optimal elements in vector optimization with variable ordering structures

  • Gabriele Eichfelder
  • Refail Kasimbeyli
    • Categories Multi-Criteria Optimization, Nonlinear Optimization Tags , , ,

    In this paper, proper optimality concepts in vector optimization with variable ordering structures are introduced for the first time and characterization results via scalarizations are given. New type of scalarizing functionals are presented and their properties are discussed. The scalarization approach suggested in the paper does not require convexity and boundedness conditions. CitationPreprint of the … Read more

    Projection: A Unified Approach to Semi-Infinite Linear Programs and Duality in Convex Programming

  • Amitabh Basu
  • Kipp Martin
  • Christopher Thomas Ryan
    • Categories Convex Optimization, Linear, Cone and Semidefinite Programming, Semi-infinite Programming Tags , , , ,

    Fourier-Motzkin elimination is a projection algorithm for solving finite linear programs. We extend Fourier-Motzkin elimination to semi-infinite linear programs which are linear programs with finitely many variables and infinitely many constraints. Applying projection leads to new characterizations of important properties for primal-dual pairs of semi-infinite programs such as zero duality gap, feasibility, boundedness, and solvability. … Read more

    An adaptive accelerated proximal gradient method and its homotopy continuation for sparse optimization

  • Qihang Lin
  • Lin Xiao
    • Categories Convex and Nonsmooth Optimization Tags , , ,

    We consider optimization problems with an objective function that is the sum of two convex terms: one is smooth and given by a black-box oracle, and the other is general but with a simple, known structure. We first present an accelerated proximal gradient (APG) method for problems where the smooth part of the objective function … Read more