(Mixed) Integer Nonlinear Programming

A Unified Approach to Mixed-Integer Optimization Problems With Logical Constraints

  • Dimitris Bertsimas
  • Ryan Cory-Wright
  • Jean Pauphilet
    • Categories (Mixed) Integer Nonlinear Programming, Cutting Plane Approaches Tags , , ,

    We propose a unified framework to address a family of classical mixed-integer optimization problems with logically constrained decision variables, including network design, facility location, unit commitment, sparse portfolio selection, binary quadratic optimization, sparse principal component analysis and sparse learning problems. These problems exhibit logical relationships between continuous and discrete variables, which are usually reformulated linearly … Read more

    Strategic Network Design for Parcel Delivery with Drones under Competition

  • Gohram Baloch
  • Fatma Gzara
    • Categories (Mixed) Integer Nonlinear Programming, Supply Chain Management, Transportation

    This paper studies the economic desirability of UAV parcel delivery and its e ect on e-retailer distribution network while taking into account technological limitations, government regulations, and customer behavior. We consider an e-retailer o ering multiple same day delivery services including a fast UAV service and develop a distribution network design formulation under service based competition where … Read more

    Theorems of the Alternative for Conic Integer Programming

  • Temitayo Ajayi
  • Andrew J. Schaefer
  • Varun Suriyanarayana
    • Categories (Mixed) Integer Nonlinear Programming Tags , ,

    Farkas’ Lemma is a foundational result in linear programming, with implications in duality, optimality conditions, and stochastic and bilevel programming. Its generalizations are known as theorems of the alternative. There exist theorems of the alternative for integer programming and conic programming. We present theorems of the alternative for conic integer programming. We provide a nested … Read more

    Solving Multiobjective Mixed Integer Convex Optimization Problems

  • Marianna De Santis
  • Gabriele Eichfelder
  • Julia Niebling
  • Stefan Rocktäschel
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Multi-Criteria Optimization Tags , ,

    Multiobjective mixed integer convex optimization refers to mathematical programming problems where more than one convex objective function needs to be optimized simultaneously and some of the variables are constrained to take integer values. We present a branch-and-bound method based on the use of properly defined lower bounds. We do not simply rely on convex relaxations, … Read more

    Multiphase Mixed-Integer Nonlinear Optimal Control of Hybrid Electric Vehicles

  • Francesco Braghin
  • Nicolò Robuschi
  • Sebastian Sager
  • Federico Cheli
  • Clemens Zeile
    • Categories (Mixed) Integer Nonlinear Programming, Control Applications, Systems governed by Differential Equations Optimization

    This paper considers the problem of computing the non-causal minimum-fuel energy management strategy of a hybrid electric vehicle on a given driving cycle. Specifically, we address the multiphase mixed-integer nonlinear optimal control problem arising when optimal gear choice, torque split and engine on/off controls are sought in off-line evaluations. We propose an efficient model by … Read more

    On the Relation between the Extended Supporting Hyperplane Algorithm and Kelley’s Cutting Plane Algorithm

  • Ambros Gleixner
  • Felipe Serrano
  • Robert Schwarz
    • Categories (Mixed) Integer Nonlinear Programming, Convex Optimization Tags , ,

    Recently, Kronqvist et al.rediscovered the supporting hyperplane algorithm of Veinott and demonstrated its computational benefits for solving convex mixed-integer nonlinear programs. In this paper we derive the algorithm from a geometric point of view. This enables us to show that the supporting hyperplane algorithm is equivalent to Kelley’s cutting plane algorithm applied to a particular … Read more

    A mixed-integer optimization approach to an exhaustive cross-validated model selection for regression

  • Dennis Kreber
    • Categories (Mixed) Integer Nonlinear Programming, Statistics Tags , , , ,

    We consider a linear regression model for which we assume that many of the observed regressors are irrelevant for the prediction. To avoid overfitting, we conduct a variable selection and only include the true predictors for the least square fitting. The best subset selection gained much interest in recent years for addressing this objective. For … Read more

    Using two-dimensional Projections for Stronger Separation and Propagation of Bilinear Terms

  • Ambros Gleixner
  • Felipe Serrano
  • Benjamin Müller
    • Categories (Mixed) Integer Nonlinear Programming, Global Optimization, Nonlinear Optimization Tags , , , , , ,

    One of the most fundamental ingredients in mixed-integer nonlinear programming solvers is the well- known McCormick relaxation for a product of two variables x and y over a box-constrained domain. The starting point of this paper is the fact that the convex hull of the graph of xy can be much tighter when computed over … Read more

    Computing Feasible Points of Bilevel Problems with a Penalty Alternating Direction Method

  • Thomas Kleinert
  • Martin Schmidt
    • Categories (Mixed) Integer Linear Programming, (Mixed) Integer Nonlinear Programming Tags , , , ,

    Bilevel problems are highly challenging optimization problems that appear in many applications of energy market design, critical infrastructure defense, transportation, pricing, etc. Often, these bilevel models are equipped with integer decisions, which makes the problems even harder to solve. Typically, in such a setting in mathematical optimization one develops primal heuristics in order to obtain … Read more

    A switching cost aware rounding method for relaxations of mixed-integer optimal control problems

  • Felix Bestehorn
  • Christoph Hansknecht
  • Christian Kirches
  • Paul Manns
    • Categories (Mixed) Integer Nonlinear Programming, Systems governed by Differential Equations Optimization Tags ,

    This article investigates a class of Mixed-Integer Optimal Control Problems (MIOCPs) with switching costs. We introduce the problem class of Minimal-Switching-Cost Optimal Control Problems (MSCP) with an objective function that consists of two summands, a continuous term depending on the state vector and an encoding of the discrete switching costs. State vectors of Mixed-Integer Optimal … Read more