(Mixed) Integer Nonlinear Programming

REDUCTION OF TWO-STAGE PROBABILISTIC OPTIMIZATION PROBLEMS WITH DISCRETE DISTRIBUTION OF RANDOM DATA TO MIXED INTEGER PROGRAMMING PROBLEMS

  • Andrey Kibzun
  • Vladimir I. Norkin
  • Andrey Naumov
    • Categories (Mixed) Integer Nonlinear Programming, Nonsmooth Optimization, Stochastic Programming Tags , , , , ,

    We consider models of two-stage stochastic programming with a quantile second stage criterion and optimization models with a chance constraint on the second stage objective function values. Such models allow to formalize requirements to reliability and safety of the system under consideration, and to optimize the system in extreme conditions. We suggest a method of … Read more

    Locally Ideal Formulations for Piecewise Linear Functions with Indicator Variables

  • Jeff Linderoth
  • James R. Luedtke
  • Srikrishna Sridhar
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering

    In this paper, we consider mixed integer linear programming (MIP) formulations for piecewise linear functions (PLFs) that are evaluated when an indicator variable is turned on. We describe modifications to standard MIP formulations for PLFs with desirable theoretical properties and superior computational performance in this context. CitationTechnical Report #1788, Computer Sciences Department, University of Wisconsin-Madison.ArticleDownload … Read more

    On reducing a quantile optimization problem with discrete distribution to a mixed integer programming problem

  • Andrey Kibzun
  • Vladimir I. Norkin
  • Andrey Naumov
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics, Stochastic Programming Tags , , , , ,

    We suggest a method for equivalent transformation of a quantile optimization problem with discrete distribution of random parameters to mixed integer programming problems. The number of additional integer (in fact boolean) variables in the equivalent problems equals to the number of possible scenarios for random data. The obtained mixed integer problems are solved by standard … Read more

    Intersection Cuts for Mixed Integer Conic Quadratic Sets

  • Kent Andersen
  • Anders Jensen
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Balas introduced intersection cuts for mixed integer linear sets. Intersection cuts are given by closed form formulas and form an important class of cuts for solving mixed integer linear programs. In this paper we introduce an extension of intersection cuts to mixed integer conic quadratic sets. We identify the formula for the conic quadratic intersection … Read more

    A New Class of Valid Inequalities for Nonlinear Network Design Problems

  • Armin Fügenschuh
  • Jesco Humpola
    • Categories (Mixed) Integer Nonlinear Programming

    We consider a nonlinear nonconvex network design problem that arises in the extension of natural gas transmission networks. Given is such network with active and passive components, that is, valves, compressors, pressure regulators (active) and pipelines (passive), and a desired amount of flow at certain specified entry and exit nodes of the network. Besides flow … Read more

    Intersection Cuts for Nonlinear Integer Programming: Convexification Techniques for Structured Sets

  • Mustafa Kilinc
  • Sina Modaresi
  • Juan Pablo Vielma
    • Categories (Mixed) Integer Nonlinear Programming

    We study the generalization of split, k-branch split, and intersection cuts from Mixed Integer Linear Programming to the realm of Mixed Integer Nonlinear Programming. Constructing such cuts requires calculating the convex hull of the difference between a convex set and an open set with a simple geometric structure. We introduce two techniques to give precise … Read more

    Quadratic Outer Approximation for Convex Integer Programming

  • Christoph Buchheim
  • Long Trieu
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Quadratic Programming Tags , ,

    We present a quadratic outer approximation scheme for solving general convex integer programs, where suitable quadratic approximations are used to underestimate the objective function instead of classical linear approximations. As a resulting surrogate problem we consider the problem of minimizing a function given as the maximum of finitely many convex quadratic functions having the same … Read more

    Asset Allocation under the Basel Accord Risk Measures

  • Xiaodi Bai
  • Xin Liu
  • Xianhua Peng
  • Zaiwen Wen
  • Xiaoling Sun
    • Categories (Mixed) Integer Nonlinear Programming, Finance and Economics Tags , , , , ,

    Financial institutions are currently required to meet more stringent capital requirements than they were before the recent financial crisis; in particular, the capital requirement for a large bank’s trading book under the Basel 2.5 Accord more than doubles that under the Basel II Accord. The significant increase in capital requirements renders it necessary for banks … Read more

    Mixed-Integer Nonlinear Optimization

  • Pietro Belotti
  • Christian Kirches
  • Sven Leyffer
  • Jeff Linderoth
  • James R. Luedtke
  • Ashutosh Mahajan
    • Categories (Mixed) Integer Nonlinear Programming Tags , , ,

    Many optimal decision problems in scientific, engineering, and public sector applications involve both discrete decisions and nonlinear system dynamics that affect the quality of the final design or plan. These decision problems lead to mixed-integer nonlinear programming (MINLP) problems that combine the combinatorial difficulty of optimizing over discrete variable sets with the challenges of handling … Read more

    Validation of Nominations in Gas Network Optimization: Models, Methods, and Solutions

  • Armin Fügenschuh
  • Björn Geißler
  • Thorsten Koch
  • Antonio Morsi
  • Marc E. Pfetsch
  • Jessica Rövekamp
  • Lars Schewe
  • Martin Schmidt
  • Nina Geissler
  • Ralf Gollmer
  • Benjamin Hiller
  • Jesco Humpola
  • Thomas Lehmann
  • Alexander Martin
  • Ruediger Schultz
  • Robert Schwarz
  • Jonas Schweiger
  • Claudia Stangl
  • Marc C. Steinbach
  • Stefan Vigerske
  • Bernhard M. Willert
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , ,

    In this article we investigate methods to solve a fundamental task in gas transportation, namely the validation of nomination problem: Given a gas transmission network consisting of passive pipelines and active, controllable elements and given an amount of gas at every entry and exit point of the network, find operational settings for all active elements … Read more