Applications – Science and Engineering

MIP-Based Instantaneous Control of Mixed-Integer PDE-Constrained Gas Transport Problems

  • Martin Gugat
  • Günter Leugering
  • Martin Schmidt
  • Mathias Sirvent
  • David Wintergerst
  • Alexander Martin
    • Categories (Mixed) Integer Nonlinear Programming, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags , , , ,

    We study the transient optimization of gas transport networks including both discrete controls due to switching of controllable elements and nonlinear fluid dynamics described by the system of isothermal Euler equations, which are partial differential equations in time and 1-dimensional space. This combination leads to mixed-integer optimization problems subject to nonlinear hyperbolic partial differential equations … Read more

    Decomposition Algorithms for Distributionally Robust Optimization using Wasserstein Metric

  • Fengqiao Luo
  • Sanjay Mehrotra
    • Categories Data-Mining, Robust Optimization, Semi-infinite Programming Tags , , , ,

    We study distributionally robust optimization (DRO) problems where the ambiguity set is de ned using the Wasserstein metric. We show that this class of DRO problems can be reformulated as semi-in nite programs. We give an exchange method to solve the reformulated problem for the general nonlinear model, and a central cutting-surface method for the convex case, … Read more

    Optimal Installation for Electric Vehicle Wireless Charging Lanes

  • Mashrur Chowdhury
  • MD Zadid Khan
  • Ilya Safro
  • Hayato Ushijima-Mwesigwa
    • Categories 0-1 Programming, Civil and Environmental Engineering, Transportation

    Range anxiety, the persistent worry about not having enough battery power to complete a trip, remains one of the major obstacles to widespread electric-vehicle adoption. As cities look to attract more users to adopt electric vehicles, the emergence of wireless in-motion car charging technology presents itself as a solution to range anxiety. For a limited … Read more

    Automatic Differentiation of the Open CASCADE Technology CAD System and its coupling with an Adjoint CFD Solver

  • Salvatore Auriemma
  • Herve Legrand
  • Mladen Banovic
  • Jens-Dominik Müller
  • Orest Mykhaskiv
  • Andrea Walther
    • Categories Optimization of Systems modeled by PDEs, Unconstrained Optimization Tags , , ,

    Automatic Differentiation (AD) is applied to the open-source CAD system Open CASCADE Technology using the AD software tool ADOL-C (Automatic Differentiation by OverLoading in C++). The differentiated CAD system is coupled with a discrete adjoint CFD solver, thus providing the first example of a complete differentiated design chain built from generic, multi-purpose tools. The design … Read more

    Random Sampling and Machine Learning to Understand Good Decompositions

  • Saverio Basso
  • Alberto Ceselli
  • Andrea Tettamanzi
    • Categories (Mixed) Integer Linear Programming, Data-Mining Tags , ,

    Motivated by its implications in the development of general purpose solvers for decomposable Mixed Integer Programs (MIP), we address a fundamental research question, that is to assess if good decomposition patterns can be consistently found by looking only at static properties of MIP input instances, or not. We adopt a data driven approach, devising a … Read more

    Polynomial-Time Methods to Solve Unimodular Quadratic Programs With Performance Guarantees

  • Edwin K.P. Chong
  • Hans D Mittelmann
  • Shankarachary Ragi
    • Categories Applications - Science and Engineering Tags , , , ,

    We develop polynomial-time heuristic methods to solve unimodular quadratic programs (UQPs) approximately, which are known to be NP-hard. In the UQP framework, we maximize a quadratic function of a vector of complex variables with unit modulus. Several problems in active sensing and wireless communication applications boil down to UQP. With this motivation, we present three … Read more

    On Procrustes matching of non-negative matrices and an application to random tomography

  • Christian Rau
    • Categories Biomedical Applications, Statistics

    We consider a Procrustes matching problem for non-negative matrices that arose in random tomography. As an alternative to the Frobenius distance, we propose an alternative non-symmetric distance using generalized inverses. Among its advantages is that it leads to a relatively simple quadratic function that can be optimized with least-square methods on manifolds. Citation Accepted for … Read more

    MPC as a DVI: Implications on Sampling Rates and Accuracy

  • Mihai Anitescu
  • Victor M. Zavala
    • Categories Chemical Engineering, Control Applications, Nonlinear Optimization

    We show that the evolution of a dynamical system driven by controls obtained by the solution of an embedded optimization problem (as done in MPC) can be cast as a differential variational inequality (DVI). The DVI abstraction reveals that standard sampled-data MPC implementations (in which the control law is computed using states that are sampled … Read more

    Learning Enabled Optimization: Towards a Fusion of Statistical Learning and Stochastic Optimization

  • Yunxiao Deng
  • Suvrajeet Sen
    • Categories Problem Solving Environments, Statistics, Stochastic Programming Tags , , ,

    Several emerging applications, such as “Analytics of Things” and “Integrative Analytics” call for a fusion of statistical learning (SL) and stochastic optimization (SO). The Learning Enabled Optimization paradigm fuses concepts from these disciplines in a manner which not only enriches both SL and SO, but also provides a framework which supports rapid model updates and … Read more

    D-OPTIMAL DESIGN FOR MULTIVARIATE POLYNOMIAL REGRESSION VIA THE CHRISTOFFEL FUNCTION AND SEMIDEFINITE RELAXATIONS

  • Yohann De Castro
  • Didier Henrion
  • Jean-Bernard Lasserre
  • Fabrice Gamboa
  • Roxana Hess
    • Categories Semi-definite Programming, Statistics

    We present a new approach to the design of D-optimal experiments with multivariate polynomial regressions on compact semi-algebraic design spaces. We apply the moment-sum-of-squares hierarchy of semidefinite programming problems to solve numerically and approximately the optimal design problem. The geometry of the design is recovered with semidefinite programming duality theory and the Christoffel polynomial. Article … Read more