Applications – Science and Engineering

A note on preconditioning weighted linear least squares, with consequences for weakly-constrained variational data assimilation

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
  • Ehouarn Simon
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares Tags , ,

    The effect of preconditioning linear weighted least-squares using an approximation of the model matrix is analyzed, showing the interplay of the eigenstructures of both the model and weighting matrices. A small example is given illustrating the resulting potential inefficiency of such preconditioners. Consequences of these results in the context of the weakly-constrained 4D-Var data assimilation … Read more

    On the use of the saddle formulation in weakly-constrained 4D-VAR data assimilation

  • Serge Gratton
  • Philippe L. Toint
  • Selime Gürol
  • Ehouarn Simon
    • Categories Basic Sciences Applications, Nonlinear Systems and Least-Squares, Unconstrained Optimization Tags , , , ,

    This paper discusses the practical use of the saddle variational formulation for the weakly-constrained 4D-VAR method in data assimilation. It is shown that the method, in its original form, may produce erratic results or diverge because of the inherent lack of monotonicity of the produced objective function values. Convergent, variationaly coherent variants of the algorithm … Read more

    Computation of exact bootstrap confidence intervals: complexity and deterministic algorithms

  • Dimitris Bertsimas
  • Bradley Sturt
    • Categories Applications - OR and Management Sciences, Approximation Algorithms, Statistics Tags , , , ,

    The bootstrap is a nonparametric approach for calculating quantities, such as confidence intervals, directly from data. Since calculating exact bootstrap quantities is believed to be intractable, randomized resampling algorithms are traditionally used. Motivated by the fact that the variability from randomization can lead to inaccurate outputs, we propose a deterministic approach. First, we establish several … Read more

    Complementarity-Based Nonlinear Programming Techniques for Optimal Mixing in Gas Networks

  • Falk M. Hante
  • Martin Schmidt
    • Categories Applications - Science and Engineering, Complementarity and Variational Inequalities, Nonlinear Optimization Tags , , , ,

    We consider nonlinear and nonsmooth mixing aspects in gas transport optimization problems. As mixed-integer reformulations of pooling-type mixing models already render small-size instances computationally intractable, we investigate the applicability of smooth nonlinear programming techniques for equivalent complementarity-based reformulations. Based on recent results for remodeling piecewise affine constraints using an inverse parametric quadratic programming approach, we … Read more

    Membership testing for Bernoulli and tail-dependence matrices

  • Daniel Krause
  • Jonas Schwinn
  • Ralf Werner
  • Matthias Scherer
    • Categories Finance and Economics, Linear Programming, Statistics Tags , , ,

    Testing a given matrix for membership in the family of Bernoulli matrices is a longstanding problem, the many applications of Bernoulli vectors in computer science, finance, medicine, and operations research emphasize its practical relevance. A novel approach towards this problem was taken by [Fiebig et al., 2017] for lowdimensional settings d

    The Trimmed Lasso: Sparsity and Robustness

  • Dimitris Bertsimas
  • Rahul Mazumder
  • Martin Copenhaver
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization, Statistics

    Nonconvex penalty methods for sparse modeling in linear regression have been a topic of fervent interest in recent years. Herein, we study a family of nonconvex penalty functions that we call the trimmed Lasso and that offers exact control over the desired level of sparsity of estimators. We analyze its structural properties and in doing … Read more

    Electric Power Infrastructure Planning: Mixed-Integer Programming Model and Nested Decomposition Algorithm

  • Ignacio E. Grossmann
  • Dimitri J. Papageorgiou
  • Cristiana L. Lara
  • D. Mallapragada
  • A. Venkatesh
    • Categories (Mixed) Integer Linear Programming, Applications - Science and Engineering Tags , , , , ,

    This paper addresses the long-term planning of electric power infrastructures considering high renewable penetration. To capture the intermittency of these sources, we propose a deterministic multi-scale Mixed-Integer Linear Programming (MILP) formulation that simultaneously considers annual generation investment decisions and hourly operational decisions. We adopt judicious approximations and aggregations to improve its tractability. Moreover, to overcome … Read more

    A Hierarchical Alternating Direction Method of Multipliers for Fully Distributed Unit Commitment

  • Zhang Chen
    • Categories Applications - Science and Engineering Tags , ,

    Abstract—This paper discusses a hierarchical alternating direction method of multipliers (ADMM) approach for the unit commitment (UC) problem in a fully distributed manner. Decentralized unit commitment operation schemes have several advantages when compared with the traditional centralized management system for smart grid. Specifically, decentralized management is more flexible, less computationally intensive, and easier to implement … Read more

    Algorithmic Results for Potential-Based Flows: Easy and Hard Cases

  • Martin Gross
  • Marc E. Pfetsch
  • Lars Schewe
  • Martin Schmidt
  • Martin Skutella
    • Categories Applications - Science and Engineering, Integer Programming, Network Optimization Tags , , , , ,

    Potential-based flows are an extension of classical network flows in which the flow on an arc is determined by the difference of the potentials of its incident nodes. Such flows are unique and arise, for example, in energy networks. Two important algorithmic problems are to determine whether there exists a feasible flow and to maximize … Read more

    A Decomposition Method for MINLPs with Lipschitz Continuous Nonlinearities

  • Martin Schmidt
  • Mathias Sirvent
  • Winnifried Wollner
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Systems governed by Differential Equations Optimization Tags , , , ,

    Many mixed-integer optimization problems are constrained by nonlinear functions that do not possess desirable analytical properties like convexity or factorability or cannot even be evaluated exactly. This is, e.g., the case for problems constrained by differential equations or for models that rely on black-box simulation runs. For these problem classes, we present, analyze, and test … Read more