Applications – Science and Engineering

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 LabbĂ©
  • 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

    Maximum-Entropy Sampling and the Boolean Quadric Polytope

  • Kurt M. Anstreicher
    • Categories (Mixed) Integer Nonlinear Programming, Semi-definite Programming, Statistics Tags , ,

    We consider a bound for the maximum-entropy sampling problem (MESP) that is based on solving a max-det problem over a relaxation of the Boolean Quadric Polytope (BQP). This approach to MESP was first suggested by Christoph Helmberg over 15 years ago, but has apparently never been further elaborated or computationally investigated. We find that the … Read more

    Approximate Positively Correlated Distributions and Approximation Algorithms for D-optimal Design

  • Mohit Singh
  • Weijun Xie
    • Categories Approximation Algorithms, Data-Mining Tags , , ,

    Experimental design is a classical problem in statistics and has also found new applications in machine learning. In the experimental design problem, the aim is to estimate an unknown vector x in m-dimensions from linear measurements where a Gaussian noise is introduced in each measurement. The goal is to pick k out of the given … Read more

    Forecasting Solar Flares using magnetogram-based predictors and Machine Learning

  • Federico Benvenuto
  • Manolis K. Georgoulis
  • D. Shaun Bloomfield
  • Kostas Florios
  • Jordan A. Guerra
  • Ioannis Kontogiannis
  • Sung-Hong Park
    • Categories Basic Sciences Applications, Data-Mining, Statistics Tags ,

    We propose a forecasting approach for solar flares based on data from Solar Cycle 24, taken by the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) mission. In particular, we use the Space-weather HMI Active Region Patches (SHARP) product that facilitates cut-out magnetograms of solar active regions (AR) in the Sun … Read more

    Model and Discretization Error Adaptivity within Stationary Gas Transport Optimization

  • Volker Mehrmann
  • Martin Schmidt
  • Jeroen J. Stolwijk
    • Categories Applications - Science and Engineering, Network Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    The minimization of operation costs for natural gas transport networks is studied. Based on a recently developed model hierarchy ranging from detailed models of instationary partial differential equations with temperature dependence to highly simplified algebraic equations, modeling and discretization error estimates are presented to control the overall error in an optimization method for stationary and … Read more

    On the local stability of semidefinite relaxations

  • Sameer Agarwal
  • Diego Cifuentes
  • Pablo A. Parrilo
  • Rekha R. Thomas
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , ,

    In this paper we consider a parametric family of polynomial optimization problems over algebraic sets. Although these problems are typically nonconvex, tractable convex relaxations via semidefinite programming (SDP) have been proposed. Often times in applications there is a natural value of the parameters for which the relaxation will solve the problem exactly. We study conditions … Read more

    Sparse principal component analysis and its l1-relaxation

  • Santanu S. Dey
  • Rahul Mazumder
  • Marco Molinaro
  • Guanyi Wang
    • Categories (Mixed) Integer Nonlinear Programming, Data-Mining

    Principal component analysis (PCA) is one of the most widely used dimensionality reduction methods in scientific data analysis. In many applications, for additional interpretability, it is desirable for the factor loadings to be sparse, that is, we solve PCA with an additional cardinality (l0) constraint. The resulting optimization problem is called the sparse principal component … Read more