Alexander Martin

Towards Simulation Based Mixed-Integer Optimization with Differential Equations

  • Martin Gugat
  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • David Wintergerst
  • Alexander Martin
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , , , ,

    We propose a decomposition based method for solving mixed-integer nonlinear optimization problems with “black-box” nonlinearities, where the latter, e.g., may arise due to differential equations or expensive simulation runs. The method alternatingly solves a mixed-integer linear master problem and a separation problem for iteratively refining the mixed-integer linear relaxation of the nonlinearity. We prove that … Read more

    Transmission and Generation Investment in Electricity Markets: The Effects of Market Splitting and Network Fee Regimes

  • Veronika Grimm
  • Martin Schmidt
  • Alexander Martin
  • Weibelzahl Martin
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Network Optimization Tags , , , , ,

    We propose an equilibrium model that allows to analyze the long-run impact of the regulatory environment on transmission line expansion by the regulator and investment in generation capacity by private firms in liberalized electricity markets. The model incorporates investment decisions of the transmission operator and private firms in expectation of an energy-only market and cost-based … Read more

    Steiner Trees with Degree Constraints: Structural Results and an Exact Solution Approach

  • Frauke Liers
  • Alexander Martin
  • Susanne Pape
    • Categories Branch and Cut Algorithms, Polyhedra Tags , , , ,

    In this paper we study the Steiner tree problem with degree constraints. Motivated by an application in computational biology we first focus on binary Steiner trees in which all node degrees are required to be at most three. We then present results for general degree-constrained Steiner trees. It is shown that finding a binary Steiner … Read more

    Polyhedral Approximation of Ellipsoidal Uncertainty Sets via Extended Formulations – a computational case study –

  • Andreas Bärmann
  • Andreas Heidt
  • Sebastian Pokutta
  • Alexander Martin
  • Christoph Thurner
    • Categories (Mixed) Integer Linear Programming, Robust Optimization, Second-Order Cone Programming Tags , , ,

    Robust optimization is an important technique to immunize optimization problems against data uncertainty. In the case of a linear program and an ellipsoidal uncertainty set, the robust counterpart turns into a second-order cone program. In this work, we investigate the efficiency of linearizing the second-order cone constraints of the latter. This is done using the … Read more

    Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions

  • Armin Fügenschuh
  • Björn Geißler
  • Thorsten Koch
  • Antonio Morsi
  • Marc E. Pfetsch
  • Jessica Rövekamp
  • Lars Schewe
  • Martin Schmidt
  • Nina Geissler
  • Ralf Gollmer
  • Benjamin Hiller
  • Jesco Humpola
  • Thomas Lehmann
  • Alexander Martin
  • Ruediger Schultz
  • Robert Schwarz
  • Jonas Schweiger
  • Claudia Stangl
  • Marc C. Steinbach
  • Stefan Vigerske
  • Bernhard M. Willert
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , ,

    In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements … Read more

    Polyhedral Aspects of Self-Avoiding Walks

  • Agnes Dittel
  • Armin Fügenschuh
  • Alexander Martin
    • Categories Cutting Plane Approaches, Polyhedra

    In this paper, we study self-avoiding walks of a given length on a graph. We consider a formulation of this problem as a binary linear program. We analyze the polyhedral structure of the underlying polytope and describe valid inequalities. Proofs for their facial properties for certain special cases are given. In a variation of this … Read more

    LP and SDP Branch-and-Cut Algorithms for the Minimum Graph Bisection Problem: A Computational Comparison

  • Marzena Fuegenschuh
  • Christoph Helmberg
  • Alexander Martin
    • Categories Branch and Cut Algorithms, Polyhedra Tags , , ,

    While semidefinite relaxations are known to deliver good approximations for combinatorial optimization problems like graph bisection, their practical scope is mostly associated with small dense instances. For large sparse instances, cutting plane techniques are considered the method of choice. These are also applicable for semidefinite relaxations via the spectral bundle method, which allows to exploit … Read more