Month: July 2019

Improved Penalty Algorithm for Mixed Integer PDE Constrained Optimization (MIPDECO) Problems

  • Dominik Garmatter
  • Margherita Porcelli
  • Francesco Rinaldi
  • Martin Stoll
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Optimization of Systems modeled by PDEs Tags , , ,

    Optimal control problems including partial differential equation (PDE) as well as integer constraints merge the combinatorial difficulties of integer programming and the challenges related to large-scale systems resulting from discretized PDEs. So far, the Branch-and-Bound framework has been the most common solution strategy for such problems. In order to provide an alternative solution approach, especially … Read more

    Distributionally robust chance constrained geometric optimization

  • Jia Liu
  • Abdel Lisser
  • Zhiping Chen
    • Categories Convex Optimization, Robust Optimization, Stochastic Programming Tags , , ,

    This paper discusses distributionally robust geometric programs with individual and joint chance constraints. Seven groups of uncertainty sets are considered: uncertainty sets with first two order moments information, uncertainty sets constrained by the Kullback-Leibler divergence distance with a normal reference distribution or a discrete reference distribution, uncertainty sets with known first moments or known first … Read more

    Mordukhovich Stationarity for Mathematical Programs with Switching Constraints under Weak Constraint Qualifications

  • Lei Guo
  • Gao-Xi Li
    • Categories Constrained Nonlinear Optimization, Nonlinear Optimization

    The mathematical program with switching constraints (MPSC), which is recently introduced, is a difficult class of optimization problems since standard constraint qualifications are very likely to fail at local minimizers. MPSC arises from the discretization of optimal control problems with switching constraints which appears frequently in the field of control. Due to the failure of … Read more

    Characterizations of explicitly quasiconvex vector functions w.r.t. polyhedral cones

  • Christian Günther
  • Nicolae Popovici
    • Categories Generalized Convexity/Monoticity

    The aim of this paper is to present new characterizations of explicitly cone-quasiconvex vector functions with respect to a polyhedral cone of a finite-dimensional Euclidean space. These characterizations are given in terms of classical explicit quasiconvexity of certain real-valued functions, defined by composing the vector-valued function with appropriate scalarization functions, namely the extreme directions of … Read more

    Dynamic Design Of Reserve Crew Duties For Long Haul Airline Crew

  • Richard Janssen
  • Bruno F. Santos
  • Lennart Scherp
    • Categories Airline Optimization, Applications - OR and Management Sciences, Scheduling

    Airlines need crew to operate their flights. In case of crew unavailability, for example due to illness, the airline often uses reserve crew to still be able to operate the flight. In this paper, we apply a simulation-based optimization method to determine how much and on which days reserve crew needs to be scheduled. This … Read more

    Tensor Methods for Finding Approximate Stationary Points of Convex Functions

  • Geovani Nunes Grapiglia
  • Yurii Nesterov
    • Categories Convex Optimization Tags , , , ,

    In this paper we consider the problem of finding \epsilon-approximate stationary points of convex functions that are p-times differentiable with \nu-Hölder continuous pth derivatives. We present tensor methods with and without acceleration. Specifically, we show that the non-accelerated schemes take at most O(\epsilon^{-1/(p+\nu-1)}) iterations to reduce the norm of the gradient of the objective below … Read more

    MIPLIB 2017: Data-Driven Compilation of the 6th Mixed-Integer Programming Library

  • Tobias Achterberg
  • Michael Bastubbe
  • Timo Berthold
  • Philipp M. Christophel
  • Gerald Gamrath
  • Ambros Gleixner
  • Gregor Hendel
  • Thorsten Koch
  • Jeff Linderoth
  • Marco E. Lübbecke
  • Hans D Mittelmann
  • Ted K. Ralphs
  • Kati Jarck
  • Derya Ozyurt
  • Domenico Salvagnin
  • Yuji Shinano
    • Categories (Mixed) Integer Linear Programming, Optimization Software Benchmark

    We report on the selection process leading to the sixth version of the Mixed Integer Programming Library. Selected from an initial pool of 5,721 instances, the new MIPLIB 2017 collection consists of 1,065 instances. A subset of 240 instances was specially selected for benchmarking solver performance. For the first time, these sets were compiled using … Read more

    Tight tail probability bounds for distribution-free decision making

  • Ruud C.M. Brekelmans
  • Dick den Hertog
  • Wouter Van Eekelen
  • Ernst Roos
  • Johan Van Leeuwaarden
    • Categories Robust Optimization, Stochastic Programming Tags , , ,

    Chebyshev’s inequality provides an upper bound on the tail probability of a random variable based on its mean and variance. While tight, the inequality has been criticized for only being attained by pathological distributions that abuse the unboundedness of the underlying support and are not considered realistic in many applications. We provide alternative tight lower … Read more

    Hub Location and Route Dimensioning: Strategic and Tactical Intermodal Transportation Hub Network Design

  • Oya Ekin Karasan
  • Hande Yaman
  • Barış Yıldız
    • Categories Applications - OR and Management Sciences, Combinatorial Optimization, Transportation Tags , , , , ,

    We propose a novel hub location model that jointly eliminates the traditional assumptions on the structure of the network and on the discount due to economies of scale in an effort to better reflect real-world logistics and transportation systems. Our model extends the hub literature in various facets: instead of connecting non-hub nodes directly to … Read more

    The stochastic multi-gradient algorithm for multi-objective optimization and its application to supervised machine learning

  • Suyun Liu
  • Luis Nunes Vicente
    • Categories Convex Optimization, Multi-Criteria Optimization, Stochastic Programming Tags , , ,

    Optimization of conflicting functions is of paramount importance in decision making, and real world applications frequently involve data that is uncertain or unknown, resulting in multi-objective optimization (MOO) problems of stochastic type. We study the stochastic multi-gradient (SMG) method, seen as an extension of the classical stochastic gradient method for single-objective optimization. At each iteration … Read more