Constrained Bundle Methods for Upper Inexact Oracles with Application to Joint Chance Constrained Energy Problems

  • Claudia Sagastizábal
  • Wim van Ackooij
    • Categories Convex and Nonsmooth Optimization, Stochastic Programming Tags , ,

    Joint chance constrained problems give rise to many algorithmic challenges. Even in the convex case, i.e., when an appropriate transformation of the probabilistic constraint is a convex function, its cutting-plane linearization is just an approximation, produced by an oracle providing subgradient and function values that can only be evaluated inexactly. As a result, the cutting-plane … Read more

    Reliable p-median facility location problem: two-stage robust models and algorithms

  • Yu An
  • Bo Zeng
  • Yu Zhang
  • Long Zhao
    • Categories Applications - OR and Management Sciences, Robust Optimization Tags , , , ,

    In this paper, we propose a set of two-stage robust optimization models to design reliable p-median facility location networks subject to disruptions. A customized column-and- constraint generation approach is implemented and shown to be more effective than Benders cutting plane method. Numerical experiments are performed on real data and management insights on system design are … Read more

    An Adaptive Augmented Lagrangian Method for Large-Scale Constrained Optimization

  • Frank E. Curtis
  • Daniel P. Robinson
  • Hao Jiang
    • Categories Nonlinear Optimization Tags , , , , ,

    We propose an augmented Lagrangian algorithm for solving large-scale constrained optimization problems. The novel feature of the algorithm is an adaptive update for the penalty parameter motivated by recently proposed techniques for exact penalty methods. This adaptive updating scheme greatly improves the overall performance of the algorithm without sacrificing the strengths of the core augmented … Read more

    The Subset Sum Game

  • Andreas Darmann
  • Gaia Nicosia
  • Ulrich Pferschy
  • Joachim Schauer
    • Categories Combinatorial Optimization, Game Theory Tags , , ,

    In this work we address a game theoretic variant of the Subset Sum problem, in which two decision makers (agents/players) compete for the usage of a common resource represented by a knapsack capacity. Each agent owns a set of integer weighted items and wants to maximize the total weight of its own items included in … Read more

    Branch-and-Cut for Complementarity-Constrained Optimization

  • Ismael de Farias
  • Ernee Kozyreff
  • Ming Zhao
    • Categories Integer Programming Tags , , , , , ,

    We report and analyze the results of our computational testing of branch-and-cut for the complementarity-constrained optimization problem (CCOP). Besides the MIP cuts commonly present in commercial optimization software, we used inequalities that explore complementarity constraints. To do so, we generalized two families of cuts proposed earlier by de Farias, Johnson, and Nemhauser that had never … Read more

    Differerential Evolution methods based on local searches

  • Marco Locatelli
  • Mirko Maischberger
  • Fabio Schoen
    • Categories Global Optimization, Stochastic Approaches Tags , , ,

    In this paper we analyze the behavior of a quite standard Differential Evolution (DE) algorithm applied to the objective function transformed by means of local searches. First some surprising results are presented which concern the application of this method to standard test functions. Later we introduce an application to disk- and to sphere-packing problems, two … Read more

    Stochastic Network Design for Disaster Preparedness

  • Xing Hong
  • Miguel A. Lejeune
  • Nilay Noyan
    • Categories Applications - Science and Engineering, Stochastic Programming

    We propose a new stochastic modeling approach for a pre-disaster relief network design problem under uncertain demand and transportation capacities. We determine the size and the location of the response facilities and the inventory levels of relief supplies at each facility with the goal of guaranteeing a certain level of network reliability. The overall objective … Read more

    Augmented Lagrangian and Alternating Direction Methods for Convex Optimization: A Tutorial and Some Illustrative Computational Results

  • Jonathan Eckstein
    • Categories Convex Optimization Tags , ,

    The alternating direction of multipliers (ADMM) is a form of augmented Lagrangian algorithm that has experienced a renaissance in recent years due to its applicability to optimization problems arising from “big data” and image processing applications, and the relative ease with which it may be implemented in parallel and distributed computational environments. This paper aims … Read more

    Robust Metric Inequalities for the Γ-Robust Network Loading Problem

  • Grit Claßen
  • Arie M.C.A. Koster
  • Manuel Kutschka
  • Issam Tahiri
    • Categories Network Optimization, Robust Optimization Tags , , ,

    In this paper, we consider the network loading problem under demand uncertainties with static routing, i.e, a single routing scheme based on the fraction of the demands has to be determined. We generalize the class of metric inequalities to the Γ-robust setting and show that they yield a formulation in the capacity space. We describe … Read more