Month: July 2020

Multi-period investment pathways – Modeling approaches to design distributed energy systems under uncertainty

  • Markus Bohlayer
  • Marco Braun
  • Adrian Bürger
  • Markus Fleschutz
  • Gregor Zöttl
    • Categories (Mixed) Integer Linear Programming, Applications - OR and Management Sciences, Stochastic Programming

    Multi-modal distributed energy system planning is applied in the context of smart grids, industrial energy supply, and in the building energy sector. In real-world applications, these systems are commonly characterized by existing system structures of different age where monitoring and investment are conducted in a closed-loop, with the iterative possibility to invest. The literature contains … Read more

    A Tractable Multi-Leader Multi-Follower Peak-Load-Pricing Model with Strategic Interaction

  • Veronika Grimm
  • Lars Schewe
  • Martin Schmidt
  • Daniel Nowak
  • Alexandra Schwartz
  • Gregor Zöttl
    • Categories Applications - OR and Management Sciences, Game Theory, Global Optimization Tags , , ,

    While single-level Nash equilibrium problems are quite well understood nowadays, less is known about multi-leader multi-follower games. However, these have important applications, e.g., in the analysis of electricity and gas markets, where often a limited number of firms interacts on various subsequent markets. In this paper, we consider a special class of two-level multi-leader multi-follower … Read more

    Sequential Quadratic Optimization for Nonlinear Equality Constrained Stochastic Optimization

  • Albert S. Berahas
  • Frank E. Curtis
  • Daniel P. Robinson
  • Baoyu Zhou
    • Categories Nonlinear Optimization Tags , ,

    Sequential quadratic optimization algorithms are proposed for solving smooth nonlinear optimization problems with equality constraints. The main focus is an algorithm proposed for the case when the constraint functions are deterministic, and constraint function and derivative values can be computed explicitly, but the objective function is stochastic. It is assumed in this setting that it … Read more

    Column-Randomized Linear Programs: Performance Guarantees and Applications

  • Yi-Chun Akchen
  • Velibor Mišić
    • Categories Linear Programming, Stochastic Programming

    We propose a randomized method for solving linear programs with a large number of columns but a relatively small number of constraints. Since enumerating all the columns is usually unrealistic, such linear programs are commonly solved by column generation, which is often still computationally challenging due to the intractability of the subproblem in many applications. … Read more

    The confined primal integral

  • Timo Berthold
  • Zsolt Csizmadia
    • Categories (Mixed) Integer Nonlinear Programming, Optimization Software Benchmark Tags , ,

    It is a challenging task to fairly compare local solvers and heuristics against each other and against global solvers. How does one weigh a faster termination time against a better quality of the found solution? In this paper, we introduce the confined primal integral, a new performance measure that rewards a balance of speed and … Read more

    A general branch-and-bound framework for continuous global multiobjective optimization

  • Gabriele Eichfelder
  • Peter Kirst
  • Oliver Stein
  • Laura Meng
    • Categories Global Optimization, Multi-Criteria Optimization, Nonlinear Optimization

    Current generalizations of the central ideas of single-objective branch-and-bound to the multiobjective setting do not seem to follow their train of thought all the way. The present paper complements the various suggestions for generalizations of partial lower bounds and of overall upper bounds by general constructions for overall lower bounds from partial lower bounds, and … Read more

    Exact Penalty Function for L21 Norm Minimization over the Stiefel Manifold

  • Nachuan Xiao
  • Xin Liu
  • Ya-xiang Yuan
    • Categories Constrained Nonlinear Optimization, Statistics Tags , , ,

    L21 norm minimization with orthogonality constraints, feasible region of which is called Stiefel manifold, has wide applications in statistics and data science. The state-of-the-art approaches adopt proximal gradient technique on either Stiefel manifold or its tangent spaces. The consequent subproblem does not have closed-form solution and hence requires an iterative procedure to solve which is … Read more

    Tutorials on Advanced Optimization Methods

  • Wei Wei
    • Categories Applications - OR and Management Sciences, Applications - Science and Engineering

    This material provides thorough tutorials on some optimization techniques frequently used in various engineering disciplines, including convex optimization, linearization technique and mixed-integer linear programming, robust optimization, and equilibrium/game problems. It discusses how to reformulate a difficult problem to a solver-compatible form via convexi cation, linearization, and decomposition, so the original problem can be reliably solved by … Read more

    Complementarity Modeling of a Ramsey-Type Equilibrium Problem with Heterogeneous Agents

  • Leonhard Frerick
  • Martin Schmidt
  • Georg Müller-Fürstenberger
  • Max Späth
    • Categories Complementarity and Variational Inequalities, Finance and Economics Tags , , ,

    We contribute to the field of Ramsey-type equilibrium models with heterogeneous agents. To this end, we state such a model in a time-continuous and time-discrete form, which in the latter case leads to a finite-dimensional mixed complementarity problem. We prove the existence of solutions of the latter problem using the theory of variational inequalities and … Read more

    No-regret Learning in Price Competitions under Consumer Reference Effects

  • Negin Golrezaei
  • Patrick Jaillet
  • Jason Cheuk Nam Liang
    • Categories Applications - OR and Management Sciences, Finance and Economics, Game Theory Tags , , ,

    We study long-run market stability for repeated price competitions between two firms, where consumer demand depends on firms’ posted prices and consumers’ price expectations called reference prices. Consumers’ reference prices vary over time according to a memory-based dynamic, which is a weighted average of all historical prices. We focus on the setting where firms are … Read more