Martin Schmidt

Deciding Feasibility of a Booking in the European Gas Market on a Cycle is in P for the Case of Passive Networks

  • Martine Labbé
  • Martin Schmidt
  • Johannes Thürauf
  • Fränk Plein
    • Categories Applications - OR and Management Sciences, Network Optimization Tags , , , , ,

    We show that the feasibility of a booking in the European entry-exit gas market can be decided in polynomial time on single-cycle networks that are passive, i.e., do not contain controllable elements. The feasibility of a booking can be characterized by solving polynomially many nonlinear potential-based flow models for computing so-called potential-difference maximizing load flow … Read more

    Gamma-Robust Linear Complementarity Problems with Ellipsoidal Uncertainty Sets

  • Vanessa Krebs
  • Martin Schmidt
  • Michael Müller
    • Categories Complementarity and Variational Inequalities, Robust Optimization, Transportation Tags , , ,

    We study uncertain linear complementarity problems (LCPs), i.e., problems in which the LCP vector q or the LCP matrix M may contain uncertain parameters. To this end, we use the concept of Gamma-robust optimization applied to the gap function formulation of the LCP. Thus, this work builds upon [16]. There, we studied Gamma-robustified LCPs for … Read more

    Nonlinear Optimization of District Heating Networks

  • Richard Krug
  • Volker Mehrmann
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , , ,

    We develop a complementarity-constrained nonlinear optimization model for the time-dependent control of district heating networks. The main physical aspects of water and heat flow in these networks are governed by nonlinear and hyperbolic 1d partial differential equations. In addition, a pooling-type mixing model is required at the nodes of the network to treat the mixing … Read more

    Optimal Design of Retailer-Prosumer Electricity Tariffs Using Bilevel Optimization

  • Veronika Grimm
  • Lars Schewe
  • Martin Schmidt
  • Galina Orlinskaya
  • Gregor Zöttl
    • Categories (Mixed) Integer Nonlinear Programming, Applications - OR and Management Sciences Tags , , , ,

    We compare various flexible tariffs that have been proposed to cost-effectively govern a prosumer’s electricity management – in particular time-of-use (TOU), critical-peak-pricing (CPP), and a real-time-pricing tariff (RTP). As the outside option, we consider a fixed-price tariff (FP) that restricts the specific characteristics of TOU, CPP, and RTP, so that the flexible tariffs are at … Read more

    Portfolio Optimization with Irreversible Long-Term Investments in Renewable Energy under Policy Risk: A Mixed-Integer Multistage Stochastic Model and a Moving-Horizon Approach

  • Nadine Gatzert
  • Martin Schmidt
  • Alexander Martin
  • Benjamin Seith
  • Nikolai Vogl
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming Tags , , , ,

    Portfolio optimization is an ongoing hot topic of mathematical optimization and management science. Due to the current financial market environment with low interest rates and volatile stock markets, it is getting more and more important to extend portfolio optimization models by other types of investments than classical assets. In this paper, we present a mixed-integer … Read more

    There’s No Free Lunch: On the Hardness of Choosing a Correct Big-M in Bilevel Optimization

  • Thomas Kleinert
  • Martine Labbé
  • Martin Schmidt
  • Fränk Plein
    • Categories (Mixed) Integer Linear Programming, Complementarity and Variational Inequalities Tags , , , ,

    One of the most frequently used approaches to solve linear bilevel optimization problems consists in replacing the lower-level problem with its Karush-Kuhn-Tucker (KKT) conditions and by reformulating the KKT complementarity conditions using techniques from mixed-integer linear optimization. The latter step requires to determine some big-M constant in order to bound the lower level’s dual feasible … Read more

    A Decomposition Heuristic for Mixed-Integer Supply Chain Problems

  • Lars Schewe
  • Martin Schmidt
  • Dieter Weninger
    • Categories (Mixed) Integer Linear Programming, Supply Chain Management Tags , , , ,

    Mixed-integer supply chain models typically are very large but are also very sparse and can be decomposed into loosely coupled blocks. In this paper, we use general-purpose techniques to obtain a block decomposition of supply chain instances and apply a tailored penalty alternating direction method, which exploits the structural properties of the decomposed instances. We … Read more

    On Electricity Market Equilibria with Storage: Modeling, Uniqueness, and a Distributed ADMM

  • Julia Grübel
  • Thomas Kleinert
  • Vanessa Krebs
  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
  • Galina Orlinskaya
    • Categories Convex Optimization, Parallel Algorithms, Quadratic Programming Tags , , , , , ,

    We consider spot-market trading of electricity including storage operators as additional agents besides producers and consumers. Storages allow for shifting produced electricity from one time period to a later one. Due to this, multiple market equilibria may occur even if classical uniqueness assumptions for the case without storages are satisfied. For models containing storage operators, … Read more

    Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method

  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , ,

    Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, etc. Often, these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization one develops primal heuristics in order to obtain … Read more

    Γ-Robust Linear Complementarity Problems

  • Vanessa Krebs
  • Martin Schmidt
    • Categories Complementarity and Variational Inequalities, Game Theory, Robust Optimization Tags , , , ,

    Complementarity problems are often used to compute equilibria made up of specifically coordinated solutions of different optimization problems. Specific examples are game-theoretic settings like the bimatrix game or energy market models like for electricity or natural gas. While optimization under uncertainties is rather well-developed, the field of equilibrium models represented by complementarity problems under uncertainty … Read more