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An Adaptive Patch Approximation Algorithm for Bicriteria Convex Mixed Integer problems

  • Erik Diessel
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    Pareto frontiers of bicriteria continuous convex problems can be efficiently computed and optimal theoretical performance bounds have been established. In the case of bicriteria mixed-integer problems, the approximation of the Pareto frontier becomes, however, significantly harder. In this paper, we propose a new algorithm for approximating the Pareto frontier of bicriteria mixed-integer programs with convex … 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

    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

    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

    Cut-Sharing Across Trees and Efficient Sequential Sampling for SDDP with Uncertainty in the RHS

  • Pedro Borges de Melo
    • Categories Dynamic Programming, Stochastic Programming

    In this paper we show that when a multistage stochastic problem with stage-wise independent realizations has only RHS uncertainties, solving one tree provides a valid lower bound for all trees with the same number of scenarios per stage without any additional computational effort. The only change to the traditional algorithm is the way cuts are … Read more

    Characterization of an Anomalous Behavior of a Practical Smoothing Technique

  • Pedro Borges de Melo
    • Categories Game Theory, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

    A practical smoothing method was analyzed and tested against state-of-the-art solvers for some non-smooth optimization problems in [BSS20a; BSS20b]. This method can be used to smooth the value functions and solution mappings of fully parameterized convex problems under mild conditions. In general, the smoothing of the value function lies from above the true value function … Read more

    An Integer Programming Approach to Deep Neural Networks with Binary Activation Functions

  • Bubacarr Bah
  • Jannis Kurtz
    • Categories (Mixed) Integer Linear Programming, Other Topics, Robust Optimization Tags , , ,

    We study deep neural networks with binary activation functions (BDNN), i.e. the activation function only has two states. We show that the BDNN can be reformulated as a mixed-integer linear program which can be solved to global optimality by classical integer programming solvers. Additionally, a heuristic solution algorithm is presented and we study the model … Read more

    A Decision Space Algorithm for Multiobjective Convex Quadratic Integer Optimization

  • Marianna De Santis
  • Gabriele Eichfelder
    • Categories (Mixed) Integer Nonlinear Programming, Multi-Criteria Optimization Tags , , ,

    We present a branch-and-bound algorithm for minimizing multiple convex quadratic objective functions over integer variables. Our method looks for efficient points by fixing subsets of variables to integer values and by using lower bounds in the form of hyperplanes in the image space derived from the continuous relaxations of the restricted objective functions. We show … Read more

    Mixed Integer Bilevel Optimization with k-optimal Follower: A Hierarchy of Bounds

  • Xueyu Shi
  • Oleg A. Prokopyev
  • Ted K. Ralphs
    • Categories (Mixed) Integer Linear Programming, Game Theory Tags ,

    We consider mixed integer bilevel linear optimization problems in which the decision variables of the lower-level (follower’s) problem are all binary. We propose a general modeling and solution framework motivated by the practical reality that in a Stackelberg game, the follower does not always solve their optimization problem to optimality. They may instead implement a … Read more

    The use of multi-criteria decision-making methods in project portfolio selection: a literature review and future research directions

  • Sarah Ben Amor
  • Makbule Kandakoglu
  • Grit Walther
    • Categories Multi-Criteria Optimization Tags , , , ,

    In most project portfolio selection (PPS) situations, the presence of multiple attributes and decision-maker preference is inevitable. As Multi-criteria Decision Analysis (MCDA) methods provide a framework well-suited to deal with these challenges in PPS problems, the use of MCDA methods in real-life PPS problems has increased in recent years. This paper provides a comprehensive literature … Read more