Approaches to iterative algorithms for solving nonlinear equations with an application in tomographic absorption spectroscopy

  • Francisco J. Aragón Artacho
  • Weiwei Cai
  • Yair Censor
  • Aviv Gibali
  • Chongyuan Shui
  • David Torregrosa-Belén
    • Categories Biomedical Applications, Constrained Nonlinear Optimization, Nonsmooth Optimization Tags , , , , , ,

    In this paper we propose an approach for solving systems of nonlinear equations without computing function derivatives. Motivated by the application area of tomographic absorption spectroscopy, which is a highly-nonlinear problem with variables coupling, we consider a situation where straightforward translation to a fixed point problem is not possible because the operators that represent the … Read more

    Considering homeowner acceptance of retrofit measures within energy supply network optimization

  • Carl Eggen
  • Moritz Link
  • Stefan Volkwein
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences, Multi-Criteria Optimization Tags , , ,

    A key factor towards a low-carbon society is energy efficient heating of private houses. The choice of heating technology as well as the decision for certain energy-efficient house renovations are made mainly by individual homeowners. In contrast, municipal energy network planning heavily depends on and strongly affects these decisions. Further, there are different conflicting objectives … Read more

    Detecting and Handling Reflection Symmetries in Mixed-Integer (Nonlinear) Programming

  • Christopher Hojny
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming

    Symmetries in mixed-integer (nonlinear) programs (MINLP), if not handled appropriately, are known to negatively impact the performance of (spatial) branch-and-bound algorithms. Usually one thus tries to remove symmetries from the problem formulation or is relying on a solver that automatically detects and handles symmetries. While modelers of a problem can handle various kinds of symmetries, … Read more

    Multistage Stochastic Facility Location under Facility Disruption Uncertainty

  • Bonn Kleiford Seranilla
  • Nils Löhndorf
    • Categories Production and Logistics, Stochastic Programming, Supply Chain Management Tags , , ,

    We consider a multistage variant of the classical stochastic capacitated facility location problem under facility disruption uncertainty. Two solution algorithms for this problem class are presented: (1) stochastic dual dynamic integer programming (SDDiP), the state-of-the-art algorithm for solving multistage stochastic integer programs, and (2) shadow price approximation (SPA), an algorithm utilizing trained parameters of the … Read more

    Understanding the Douglas-Rachford splitting method through the lenses of Moreau-type envelopes

  • Felipe Atenas
    • Categories Convex and Nonsmooth Optimization, Generalized Convexity/Monoticity, Nonsmooth Optimization Tags , , , ,

    We analyze the Douglas-Rachford splitting method for weakly convex optimization problems, by the token of the Douglas-Rachford envelope, a merit function akin to the Moreau envelope. First, we use epi-convergence techniques to show that this artifact approximates the original objective function via epigraphs. Secondly, we present how global convergence and local linear convergence rates for … Read more

    Solving the parallel processor scheduling and bin packing problems with contiguity constraints: mathematical models and computational studies

  • FB Akcay
  • Maxence Delorme
    • Categories Combinatorial Optimization, Integer Programming Tags , , ,

    The parallel processor scheduling and bin packing problems with contiguity constraints are important in the field of combinatorial optimization because both problems can be used as components of effective exact decomposition approaches for several two-dimensional packing problems. In this study, we provide an extensive review of existing mathematical formulations for the two problems, together with … Read more

    A computational study of cutting-plane methods for multi-stage stochastic integer programs

  • Akul Bansal
  • Simge Küçükyavuz
    • Categories Stochastic Programming Tags , ,

    We report a computational study of cutting plane algorithms for multi-stage stochastic mixed-integer programming models with the following cuts: (i) Benders’, (ii) Integer L-shaped, and (iii) Lagrangian cuts. We first show that Integer L-shaped cuts correspond to one of the optimal solutions of the Lagrangian dual problem, and, therefore, belong to the class of Lagrangian … Read more

    Spatial branch-and-bound for nonconvex separable piecewise linear optimization

  • Thomas Hübner
  • Akshay Gupte
  • Steffen Rebennack
    • Categories (Mixed) Integer Linear Programming, Global Optimization Tags , , , ,

    Nonconvex separable piecewise linear functions (PLFs) frequently appear in applications and to approximate nonlinearitites. The standard practice to formulate nonconvex PLFs is from the perspective of discrete optimization, using special ordered sets and mixed integer linear programs (MILPs). In contrast, we take the viewpoint of global continuous optimization and present a spatial branch-and-bound algorithm (sBB) … Read more

    Extended Formulations for Control Languages Defined by Finite-State Automata

  • Christoph Buchheim
  • Maximilian Merkert
    • Categories (Mixed) Integer Linear Programming, Optimization of Systems modeled by PDEs, Polyhedra Tags , , , ,

    Many discrete optimal control problems feature combinatorial constraints on the possible switching patterns, a common example being minimum dwell-time constraints. After discretizing to a finite time grid, for these and many similar types of constraints, it is possible to give a description of the convex hull of feasible (finite-dimensional) binary controls via extended formulations. In … Read more

    Edge expansion of a graph: SDP-based computational strategies

  • Akshay Gupte
  • Melanie Siebenhofer
  • Angelika Wiegele
    • Categories Combinatorial Optimization, Parallel Algorithms, Semi-definite Programming Tags , , , ,

    Computing the edge expansion of a graph is a famously hard combinatorial problem for which there have been many approximation studies. We present two variants of exact algorithms using semidefinite programming (SDP) to compute this constant for any graph. The first variant uses the SDP relaxation first to reduce the search space considerably. The problem … Read more