Year: 2021

Distributionally Favorable Optimization: A Framework for Data-driven Decision-making with Endogenous Outliers

  • Nan Jiang
  • Weijun Xie
    • Categories Robust Optimization, Stochastic Programming Tags , , , ,

    A typical data-driven stochastic program aims to seek the best decision that minimizes the sum of a deterministic cost function and an expected recourse function under a given distribution. Recently, much success has been witnessed in the development of Distributionally Robust Optimization (DRO), which considers the worst-case expected recourse function under the least favorable probability … Read more

    A Branch & Bound Algorithm for Robust Binary Optimization with Budget Uncertainty

  • Christina Büsing
  • Timo Gersing
  • Arie M.C.A. Koster
    • Categories 0-1 Programming, Branch and Cut Algorithms, Robust Optimization Tags , , , ,

    Since its introduction in the early 2000s, robust optimization with budget uncertainty has received a lot of attention. This is due to the intuitive construction of the uncertainty sets and the existence of a compact robust reformulation for (mixed-integer) linear programs. However, despite its compactness, the reformulation performs poorly when solving robust integer problems due … Read more

    ADMM-based Unit and Time Decomposition for Price Arbitrage by Cooperative Price-Maker Electricity Storage Units

  • Miguel F. Anjos
  • James Cruise
  • Albert Solà Vilalta
    • Categories Convex Optimization, Dynamic Programming, Energy Tags , , , , , , ,

    Decarbonization via the integration of renewables poses significant challenges for electric power systems, but also creates new market opportunities. Electric energy storage can take advantage of these opportunities while providing flexibility to power systems that can help address these challenges. We propose a solution method for the optimal control of multiple price-maker electric energy storage … Read more

    An Overview of Nested Decomposition for Multi-Level Optimization Problems

  • Stephen J. Maher
  • Ibrahim Muter
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Integer Programming Tags , , , ,

    Nested multi-level structures are frequently encountered in many real-world optimization problems. Decomposition techniques are a commonly applied approach used to handle nested multi-level structures; however, the typical problem-specific focus of such techniques has led to numerous specialized formulations and solution methods. This lack of generalized results for nested multi-level optimization problems is addressed in this … Read more

    Efficient and Robust Mixed-Integer Optimization Methods for Training Binarized Deep Neural Networks

  • Jannis Kurtz
  • Bubacarr Bah
    • Categories Applications - OR and Management Sciences, Integer Programming, Robust Optimization Tags ,

    Compared to classical deep neural networks its binarized versions can be useful for applications on resource-limited devices due to their reduction in memory consumption and computational demands. In this work we study deep neural networks with binary activation functions and continuous or integer weights (BDNN). We show that the BDNN can be reformulated as a … Read more

    Differential Privacy in Multi-Party Resource Sharing

  • Utku Karaca
  • Ş. İlker Birbil
  • Nursen Aydin
  • Gizem Mullaoğlu
  • Sinan Yıldırım
    • Categories Applications - OR and Management Sciences Tags , , ,

    This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange information to obtain the optimal objective function value. This information bears private data from each party in terms of … Read more

    Exact computation of an error bound for a generalized linear complementarity problem with unique solution

  • Jean-Pierre Dussault
  • Jean Charles Gilbert
    • Categories Complementarity and Variational Inequalities Tags , , , , , , , , ,

    This paper considers a generalized form of the standard linear complementarity problem with unique solution and provides a more precise expression of an upper error bound discovered by Chen and Xiang in 2006. This expression has at least two advantages. It makes possible the exact computation of the error bound factor and it provides a … Read more

    An Integrated Rolling Horizon and Adaptive-Refinement Approach for Disjoint Trajectories Optimization

  • Benno Hoch
  • Frauke Liers
    • Categories Applications - OR and Management Sciences Tags , , , ,

    Planning of trajectories, i.e. paths over time, is a challenging task. Thereby, the trajectories for involved commodities often have to be considered jointly as separation constraints have to be respected. This is for example the case in robot motion or air traffic management. Involving these discrete separation constraints in the planning of best possible continuous … Read more

    A Theoretical and Computational Analysis of Full Strong-Branching

  • Santanu S. Dey
  • Yatharth Dubey
  • Marco Molinaro
  • Prachi Shah
    • Categories Branch and Cut Algorithms, Integer Programming Tags , , ,

    Full strong-branching (henceforth referred to as strong-branching) is a well-known variable selection rule that is known experimentally to produce significantly smaller branch-and-bound trees in comparison to all other known variable selection rules. In this paper, we attempt an analysis of the performance of the strong-branching rule both from a theoretical and a computational perspective. On … Read more

    MPCC Strategies for Nonsmooth NLPs

  • Kexin Wang
  • Lorenz T. Biegler
    • Categories Complementarity and Variational Inequalities, Nonsmooth Optimization Tags , , ,

    This paper develops solution strategies for large-scale nonsmooth optimization problems. We transform nonsmooth programs into equivalent mathematical programs with complementarity constraints (MPCCs), and then employ NLP-based strategies for their so- lution. For this purpose, two NLP formulations based on complementarity relaxations are put forward, one of which applies a parameterized formulation and operates with a … Read more