piecewise linear approximation

Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part II

  • Ben Beach
  • Robert Burlacu
  • Andreas Bärmann
  • Lukas Hager
  • Robert Hildebrand
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Quadratic Programming Tags , , , ,

    Abstract. This is Part II of a study on mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We set the focus on MIP relaxation methods for non-convex continuous variable products and extend the well-known MIP relaxation normalized multiparametric disaggregation technique (NMDT), applying a sophisticated discretization to both … Read more

    Enhancements of Discretization Approaches for Non-Convex Mixed-Integer Quadratically Constraint Quadratic Programming: Part I

  • Ben Beach
  • Robert Burlacu
  • Andreas Bärmann
  • Lukas Hager
  • Robert Hildebrand
    • Categories (Mixed) Integer Nonlinear Programming, Quadratic Programming Tags , , , ,

    We study mixed-integer programming (MIP) relaxation techniques for the solution of non-convex mixed-integer quadratically constrained quadratic programs (MIQCQPs). We present MIP relaxation methods for non-convex continuous variable products. In Part I, we consider MIP relaxations based on separable reformulation. The main focus is the introduction of the enhanced separable MIP relaxation for non-convex quadratic products … Read more

    New Algorithm to Solve Mixed Integer Quadratically Constrained Quadratic Programming Problems Using Piecewise Linear Approximation

  • Loay Alkhalifa
  • Hans D Mittelmann
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Techniques and methods of linear optimization underwent a significant improvement in the 20th century which led to the development of reliable mixed integer linear programming (MILP) solvers. It would be useful if these solvers could handle mixed integer nonlinear programming (MINLP) problems. Piecewise linear approximation (PLA) is one of most popular methods used to transform … Read more

    Utility Preference Robust Optimization with Moment-Type Information Structure

  • Shaoyan Guo
  • Huifu Xu
    • Categories Robust Optimization Tags , , , , ,

    Utility preference robust optimization (PRO) models are recently proposed to deal with decision making problems where the decision maker’s true utility function is unknown and the optimal decision is based on the worst case utility function from an ambiguity set of utility functions. In this paper, we consider the case where the ambiguity set is … Read more

    Sparse Poisson regression via mixed-integer optimization

  • Kota Kudo
  • Yuichi Takano
  • Hiroki Saishu
    • Categories Integer Programming, Statistics Tags , , ,

    We present a mixed-integer optimization (MIO) approach to sparse Poisson regression. The MIO approach to sparse linear regression was first proposed in the 1970s, but has recently received renewed attention due to advances in optimization algorithms and computer hardware. In contrast to many sparse estimation algorithms, the MIO approach has the advantage of finding the … Read more

    MIQP-Based Algorithm for the Global Solution of Economic Dispatch Problems with Valve-Point Effects

  • Pierre-Antoine Absil
  • Benoît Sluysmans
  • Nicolas Stevens
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Global Optimization Tags , , , ,

    Even in a static setting, the economic load dispatch problem (ELDP)—namely the cost-optimal distribution of power among generating units to meet a specific demand subject to system constraints—turns out to be a challenge owing to the consideration of valve-point effects (VPE), which make the cost function nonsmooth and nonconvex. We present a new method, termed … Read more

    Solving Mixed-Integer Nonlinear Programs using Adaptively Refined Mixed-Integer Linear Programs

  • Robert Burlacu
  • Björn Geißler
  • Lars Schewe
    • Categories (Mixed) Integer Nonlinear Programming Tags , , , ,

    We propose a method for solving mixed-integer nonlinear programs (MINLPs) to global optimality by discretization of occuring nonlinearities. The main idea is based on using piecewise linear functions to construct mixed-integer linear program (MIP) relaxations of the underlying MINLP. In order to find a global optimum of the given MINLP we develope an iterative algorithm … Read more

    Joint rectangular geometric chance constrained programs

  • Zhiping Chen
  • Abdel Lisser
  • Jia Liu
  • Chuan Xu
    • Categories Stochastic Programming Tags , , ,

    This paper discusses joint rectangular geometric chance constrained programs. When the stochastic parameters are elliptically distributed and pairwise independent, we present a reformulation of the joint rectangular geometric chance constrained programs. As the reformulation is not convex, we propose new convex approximations based on variable transformation together with piecewise linear approximation method. Our results show … Read more

    Mixed-Integer Linear Methods for Layout-Optimization of Screening Systems in Recovered Paper Production

  • Armin Fügenschuh
  • Christine Hayn
  • Dennis Michaels
    • Categories (Mixed) Integer Nonlinear Programming, Mechanical Engineering Tags , , , , , ,

    The industrial treatment of waste paper in order to regain valuable fibers from which recovered paper can be produced, involves several steps of preparation. One important step is the separation of stickies that are normally attached to the paper. If not properly separated, remaining stickies reduce the quality of the recovered paper or even disrupt … Read more