mixed-integer nonlinear programming

Time-Domain Decomposition for Mixed-Integer Optimal Control Problems

  • Falk M. Hante
  • Richard Krug
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags , , ,

    We consider mixed-integer optimal control problems, whose optimality conditions involve global combinatorial optimization aspects for the corresponding Hamiltonian pointwise in time. We propose a time-domain decomposition, which makes this problem class accessible for mixed-integer programming using parallel-in-time direct discretizations. The approach is based on a decomposition of the optimality system and the interpretation of the … Read more

    Projective Cutting Planes for General QP with Indicator Constraints

  • Ulf Friedrich
  • Dennis Kreber
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    General quadratic optimization problems with linear constraints and additional indicator constraints on the variables are studied. Based on the well-known perspective reformulation for mixed-integer quadratic optimization problems, projective cuts are introduced as new valid inequalities for the general problem. The key idea behind the theory of these cutting planes is the projection of the continuous … Read more

    A Generic Optimization Framework for Resilient Systems

  • Marc E. Pfetsch
  • Andreas Schmitt
    • Categories (Mixed) Integer Nonlinear Programming, Robust Optimization Tags , , , ,

    This paper addresses the optimal design of resilient systems, in which components can fail. The system can react to failures and its behavior is described by general mixed integer nonlinear programs, which allows for applications to many (technical) systems. This then leads to a three-level optimization problem. The upper level designs the system minimizing a … Read more

    A Computational Study of Perspective Cuts

  • Ksenia Bestuzheva
  • Ambros Gleixner
  • Stefan Vigerske
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches, Optimization Software and Modeling Systems Tags , , ,

    The benefits of cutting planes based on the perspective function are well known for many specific classes of mixed-integer nonlinear programs with on/off structures. However, we are not aware of any empirical studies that evaluate their applicability and computational impact over large, heterogeneous test sets in general-purpose solvers. This paper provides a detailed computational study … Read more

    Sequential Competitive Facility Location: Exact and Approximate Algorithms

  • Mingyao Qi
  • Ruiwei Jiang
  • Siqian Shen
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization, Facility Planning and Design Tags , , , , ,

    We study a competitive facility location problem (CFLP), where two firms sequentially open new facilities within their budgets, in order to maximize their market shares of demand that follows a probabilistic choice model. This process is a Stackelberg game and admits a bilevel mixed-integer nonlinear program (MINLP) formulation. We derive an equivalent, single-level MINLP reformulation … Read more

    Learning Symbolic Expressions: Mixed-Integer Formulations, Cuts, and Heuristics

  • Prasanna Balaprakash
  • Sven Leyffer
  • Jongeun Kim
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering Tags , , ,

    In this paper we consider the problem of learning a regression function without assuming its functional form. This problem is referred to as symbolic regression. An expression tree is typically used to represent a solution function, which is determined by assigning operators and operands to the nodes. The symbolic regression problem can be formulated as … Read more

    An Exact Projection-Based Algorithm for Bilevel Mixed-Integer Problems with Nonlinearities

  • Maximilian Merkert
  • Galina Orlinskaya
  • Dieter Weninger
    • Categories (Mixed) Integer Nonlinear Programming, Game Theory, Global Optimization Tags , , , ,

    We propose an exact global solution method for bilevel mixed-integer optimization problems with lower-level integer variables and including nonlinear terms such as, \eg, products of upper-level and lower-level variables. Problems of this type are extremely challenging as a single-level reformulation suitable for off-the-shelf solvers is not available in general. In order to solve these problems … Read more

    Solving AC Optimal Power Flow with Discrete Decisions to Global Optimality

  • Kevin-Martin Aigner
  • Robert Burlacu
  • Frauke Liers
  • Alexander Martin
    • Categories (Mixed) Integer Nonlinear Programming, Second-Order Cone Programming Tags , , , , , , ,

    We present a solution framework for general alternating current optimal power flow (AC OPF) problems that include discrete decisions. The latter occur, for instance, in the context of the curtailment of renewables or the switching of power generation units and transmission lines. Our approach delivers globally optimal solutions and is provably convergent. We model AC … Read more

    Global Optimization for the Multilevel European Gas Market System with Nonlinear Flow Models on Trees

  • Lars Schewe
  • Martin Schmidt
  • Johannes Thürauf
    • Categories Applications - OR and Management Sciences, Global Optimization, Robust Optimization Tags , , , ,

    The European gas market is implemented as an entry-exit system, which aims to decouple transport and trading of gas. It has been modeled in the literature as a multilevel problem, which contains a nonlinear flow model of gas physics. Besides the multilevel structure and the nonlinear flow model, the computation of so-called technical capacities is … Read more

    On Refinement Strategies for Solving MINLPs by Piecewise Linear Relaxations: A Generalized Red Refinement

  • Robert Burlacu
    • Categories (Mixed) Integer Nonlinear Programming Tags , , ,

    We investigate the generalized red refinement for n-dimensional simplices that dates back to Freudenthal in a mixed-integer nonlinear program (MINLP) context. We show that the red refinement meets sufficient convergence conditions for a known MINLP solution framework that is essentially based on solving piecewise linear relaxations. In addition, we prove that applying this refinement procedure … Read more