(Mixed) Integer Nonlinear Programming

A relax-fix-and-exclude algorithm for an MINLP problem with multilinear interpolations

  • Bruno Machado Pacheco
  • Laio Seman
    • Categories (Mixed) Integer Nonlinear Programming, Chemical Engineering, Global Optimization Applications Tags , ,

    This paper introduces a novel algorithm for Mixed-Integer Nonlinear Programming (MINLP) problems with multilinear interpolations of look-up tables. These problems arise when objectives or constraints contain black-box functions only known at a finite set of evaluations on a predefined grid. We derive a piecewise-linear relaxation for the multilinear interpolants, which require an MINLP formulation. Supported … Read more

    Alternating Methods for Large-Scale AC Optimal Power Flow with Unit Commitment

  • Matthew Brun
  • Thomas Lee
  • Dirk Lauinger
  • Xin Chen
  • Xu Andy Sun
    • Categories (Mixed) Integer Nonlinear Programming, Energy Tags , , ,

    Security-constrained unit commitment with alternating current optimal power flow (SCUC-ACOPF) is a central problem in power grid operations that optimizes commitment and dispatch of generators under a physically accurate power transmission model while encouraging robustness against component failures.  SCUC-ACOPF requires solving large-scale problems that involve multiple time periods and networks with thousands of buses within … Read more

    A Graphical Global Optimization Framework for Parameter Estimation of Statistical Models with Nonconvex Regularization Functions

  • Danial Davarnia
    • Categories (Mixed) Integer Nonlinear Programming, Branch and Cut Algorithms, Global Optimization Theory Tags , , , ,

    Optimization problems with norm-bounding constraints appear in various applications, from portfolio optimization to machine learning, feature selection, and beyond. A widely used variant of these problems relaxes the norm-bounding constraint through Lagrangian relaxation and moves it to the objective function as a form of penalty or regularization term. A challenging class of these models uses … Read more

    Quadratic Convex Reformulations for MultiObjective Binary Quadratic Programming

  • Marianna De Santis
  • Lucas Létocart
  • Yue Zhang
    • Categories (Mixed) Integer Nonlinear Programming, 0-1 Programming, Multi-Criteria Optimization Tags , , ,

    Multiobjective binary quadratic programming refers to optimization problems involving multiple quadratic – potentially non-convex – objective functions and a feasible set that includes binary constraints on the variables. In this paper, we extend the well-established Quadratic Convex Reformulation technique, originally developed for single-objective binary quadratic programs, to the multiobjective setting. We propose a branch-and-bound algorithm … Read more

    Strong Formulations and Algorithms for Regularized A-Optimal Design

  • Yongchun Li
    • Categories (Mixed) Integer Nonlinear Programming, Combinatorial Optimization Tags , , , ,

    We study the Regularized A-Optimal Design (RAOD) problem, which selects a subset of \(k\) experiments to minimize the inverse of the Fisher information matrix, regularized with a scaled identity matrix. RAOD has broad applications in Bayesian experimental design, sensor placement, and cold-start recommendation. We prove its NP-hardness via a reduction from the independent set problem. … Read more

    Rank-one convexification for convex quadratic optimization with step function penalties

  • Andrés Gómez
  • Shaoning Han
    • Categories (Mixed) Integer Nonlinear Programming, Data Science Applications, Semi-definite Programming Tags ,

    We investigate convexification in convex quadratic optimization with step function penalties. Such problems can be cast as mixed-integer quadratic optimization problems, where binary variables are used to encode the non-convex step function. First, we derive the convex hull for the epigraph of a quadratic function defined by a rank-one matrix. Using this rank-one convexification, we … Read more

    Pareto Leap: An Algorithm for Biobjective Mixed-Integer Programming

  • Philip de Castro
  • Margaret Wiecek
    • Categories (Mixed) Integer Nonlinear Programming, Integer Programming, Multi-Criteria Optimization Tags , , ,

    Many real-life optimization problems need to make decisions with discrete variables and multiple, conflicting objectives. Due to this need, the ability to solve such problems is an important and active area of research. We present a new algorithm, called Pareto Leap, for identifying the (weak) Pareto slices of biobjective mixed-integer programs (BOMIPs), even when Pareto … Read more

    Integer Control Approximations for Graphon Dynamical Systems

  • Martin T. Köhler
  • Artemi Makarow
  • Christian Kirches
    • Categories (Mixed) Integer Nonlinear Programming, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Graphons generalize graphs and define a limit object of a converging graph sequence. The notion of graphons allows for a generic representation of coupled network dynamical systems. We are interested in approximating integer controls for graphon dynamical systems. To this end, we apply a decomposition approach comprised of a relaxation and a reconstruction step. We … Read more

    Operationalizing Experimental Design: Data Collection for Remote Ocean Monitoring

  • Jean Pauphilet
  • Baizhi Song
    • Categories (Mixed) Integer Nonlinear Programming, Statistics, Transportation Tags , , , ,

    Problem definition: To collect data on ocean plastic pollution and build more accurate predictive models, we need to manually take high-resolution pictures of the sea surface via floating or flying drones. Operating these vehicles, like many data collection problems in agriculture or environmental science, challenges the traditional optimal experimental design (OED) formulation from statistics by … Read more

    Lagrangian Duality for Mixed-Integer Semidefinite Programming: Theory and Algorithms

  • Frank de Meijer
  • Renata Sotirov
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming Tags , , ,

    This paper presents the Lagrangian duality theory for mixed-integer semidefinite programming (MISDP). We derive the Lagrangian dual problem and prove that the resulting Lagrangian dual bound dominates the bound obtained from the continuous relaxation of the MISDP problem. We present a hierarchy of Lagrangian dual bounds by exploiting the theory of integer positive semidefinite matrices … Read more