Applications – Science and Engineering

Tight-and-cheap conic relaxation for the AC optimal power flow problem

  • Miguel F. Anjos
  • Christian Bingane
  • Sébastien Le Digabel
    • Categories Applications - Science and Engineering, Nonlinear Optimization, Semi-definite Programming Tags , , ,

    The classical alternating current optimal power flow problem is highly nonconvex and generally hard to solve. Convex relaxations, in particular semidefinite, second-order cone, convex quadratic, and linear relaxations, have recently attracted significant interest. The semidefinite relaxation is the strongest among them and is exact for many cases. However, the computational efficiency for solving large-scale semidefinite … Read more

    Bounding and Counting Linear Regions of Deep Neural Networks

  • Srikumar Ramalingam
  • Thiago Serra
  • Christian Tjandraatmadja
    • Categories (Mixed) Integer Linear Programming, Statistics Tags , , , ,

    We investigate the complexity of deep neural networks (DNN) that represent piecewise linear (PWL) functions. In particular, we study the number of linear regions, i.e. pieces, that a PWL function represented by a DNN can attain, both theoretically and empirically. We present (i) tighter upper and lower bounds for the maximum number of linear regions … Read more

    Smart “Predict, then Optimize”

  • Adam N. Elmachtoub
  • Paul Grigas
    • Categories Applications - OR and Management Sciences, Data-Mining, Statistics

    Many real-world analytics problems involve two significant challenges: prediction and optimization. Due to the typically complex nature of each challenge, the standard paradigm is to predict, then optimize. By and large, machine learning tools are intended to minimize prediction error and do not account for how the predictions will be used in a downstream optimization … Read more

    A Random Block-Coordinate Douglas-Rachford Splitting Method with Low Computational Complexity for Binary Logistic Regression

  • Luis M. Briceno-Arias
  • Émilie Chouzenoux
  • Jean-Christophe Pesquet
  • Giovanni Chierchia
    • Categories Convex Optimization, Statistics Tags , , ,

    In this paper, we propose a new optimization algorithm for sparse logistic regression based on a stochastic version of the Douglas Rachford splitting method. Our algorithm sweeps the training set by randomly selecting a mini-batch of data at each iteration, and it allows us to update the variables in a block coordinate manner. Our approach … Read more

    GEP-MSCRA for computing the group zero-norm regularized least squares estimator

  • Shaohua Pan
  • Shujun Shujun
    • Categories Nonsmooth Optimization, Statistics

    This paper concerns with the group zero-norm regularized least squares estimator which, in terms of the variational characterization of the zero-norm, can be obtained from a mathematical program with equilibrium constraints (MPEC). By developing the global exact penalty for the MPEC, this estimator is shown to arise from an exact penalization problem that not only … Read more

    Sum of squares certificates for stability of planar, homogeneous, and switched systems

  • Amir Ali Ahmadi
  • Pablo A. Parrilo
    • Categories Control Applications, Semi-definite Programming, Systems governed by Differential Equations Optimization Tags , , ,

    We show that existence of a global polynomial Lyapunov function for a homogeneous polynomial vector field or a planar polynomial vector field (under a mild condition) implies existence of a polynomial Lyapunov function that is a sum of squares (sos) and that the negative of its derivative is also a sum of squares. This result … Read more

    Deterministic Global Optimization with Artificial Neural Networks Embedded

  • Alexander Mitsos
  • Artur M Schweidtmann
    • Categories Chemical Engineering, Global Optimization, Nonlinear Optimization Tags , , , , , , ,

    Artificial neural networks (ANNs) are used in various applications for data-driven black-box modeling and subsequent optimization. Herein, we present an efficient method for deterministic global optimization of ANN embedded optimization problems. The proposed method is based on relaxations of algorithms using McCormick relaxations in a reduced-space [\textit{SIOPT}, 20 (2009), pp. 573-601] including the convex and … Read more

    Load Scheduling for Residential Demand Response on Smart Grids

  • Miguel F. Anjos
  • Luce Brotcorne
  • Martine Labbé
  • Maria I. Restrepo
    • Categories (Mixed) Integer Linear Programming, Energy Tags , , ,

    The residential load scheduling problem is concerned with finding an optimal schedule for the operation of residential loads so as to minimize the total cost of energy while aiming to respect a prescribed limit on the power level of the residence. We propose a mixed integer linear programming formulation of this problem that accounts for … Read more

    A decentralized framework for the optimal coordination of distributed energy resources

  • Miguel F. Anjos
  • Andrea Lodi
  • Mathieu Tanneau
    • Categories (Mixed) Integer Linear Programming, Energy Tags , , , , ,

    Demand-response aggregators are faced with the challenge of how to best manage numerous and heterogeneous Distributed Energy Resources (DERs). This paper proposes a decentralized methodology for optimal coordination of DERs. The proposed approach is based on Dantzig-Wolfe decomposition and column generation, thus allowing to integrate any type of resource whose operation can be formulated within … Read more

    Mixed-Integer PDE-Constrained Optimal Control of Gas Networks

  • Mirko Hahn
  • Sven Leyffer
  • Victor M. Zavala
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , ,

    We develop a mixed-integer optimal control model with partial differential equation (PDE) constraints for gas transport networks, designed for controlling extreme state transitions, such as flow reversals. Our model shows how to combine binary compressor controls with PDE flow models. We model the flow of gas using a variant of the Euler equations, which we … Read more