Applications – Science and Engineering

Solving Power-Constrained Gas Transportation Problems using an MIP-based Alternating Direction Method

  • Björn Geißler
  • Antonio Morsi
  • Lars Schewe
  • Martin Schmidt
    • Categories (Mixed) Integer Nonlinear Programming, Applications - Science and Engineering, Constrained Nonlinear Optimization Tags , , , ,

    We present a solution algorithm for problems from steady-state gas transport optimization. Due to nonlinear and nonconvex physics and engineering models as well as discrete controllability of active network devices, these problems lead to hard nonconvex mixed-integer nonlinear optimization models. The proposed method is based on mixed-integer linear techniques using piecewise linear relaxations of the … Read more

    Sequential Threshold Control in Descent Splitting Methods for Decomposable Optimization Problems

  • Igor V. Konnov
    • Categories Constrained Nonlinear Optimization, Data-Mining, Nonsmooth Optimization

    We suggest a modification of the descent splitting methods for decomposable composite optimization problems, which maintains the basic convergence properties, but enables one to reduce the computational expenses per iteration and to provide computations in a distributed manner. It consists in making coordinate-wise steps together with a special threshold control. Citation Kazan Federal University, Kazan … Read more

    Stochastic Compositional Gradient Descent: Algorithms for Minimizing Compositions of Expected-Value Functions

  • Ethan Fang
  • Mengdi Wang
  • Han Liu
    • Categories Convex Optimization, Statistics, Stochastic Programming Tags , , , ,

    Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value functions, i.e., problems of the form $\min_x \E_v\[f_v\big(\E_w [g_w(x)]\big) \]$. In order to solve this stochastic composition problem, we propose a class … Read more

    Linear conic optimization for inverse optimal control

  • Didier Henrion
  • Jean-Bernard Lasserre
  • Edouard Pauwels
    • Categories Control Applications, Semi-definite Programming

    We address the inverse problem of Lagrangian identification based on trajectories in the context of nonlinear optimal control. We propose a general formulation of the inverse problem based on occupation measures and complementarity in linear programming. The use of occupation measures in this context offers several advantages from the theoretical, numerical and statistical points of … Read more

    HIPAD – A Hybrid Interior-Point Alternating Direction algorithm for knowledge-based SVM and feature selection

  • Ioannis G. Akrotirianakis
  • Zhiwei (Tony) Qin
  • Amit Chakraborty
  • Xiaocheng Tang
    • Categories Convex and Nonsmooth Optimization, Data-Mining, Quadratic Programming Tags , , , ,

    We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipliers in the first phase, followed by an interior-point method … Read more

    Semi-definite relaxations for optimal control problems with oscillation and concentration effects

  • Mathieu Claeys
  • Didier Henrion
  • Martin Kružík
    • Categories Control Applications, Semi-definite Programming

    Converging hierarchies of finite-dimensional semi-definite relaxations have been proposed for state-constrained optimal control problems featuring oscillation phenomena, by relaxing controls as Young measures. These semi-definite relaxations were later on extended to optimal control problems depending linearly on the control input and typically featuring concentration phenomena, interpreting the control as a measure of time with a … Read more

    High Detail Stationary Optimization Models for Gas Networks: Validation and Results

  • Martin Schmidt
  • Marc C. Steinbach
  • Bernhard M. Willert
    • Categories Applications - Science and Engineering, Constrained Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , ,

    Due to strict regulatory rules in combination with complex nonlinear physics, major gas network operators in Germany and Europe face hard planning problems that call for optimization. In part 1 of this paper we have developed a suitable model hierarchy for that purpose. Here we consider the more practical aspects of modeling. We validate individual … Read more

    A Flexible Iterative Solver for Nonconvex, Equality-Constrained Quadratic Subproblems

  • Alp Dener
  • Jason Hicken
    • Categories Constrained Nonlinear Optimization, Multidisciplinary Design Optimization, Optimization of Systems modeled by PDEs Tags , , , , ,

    We present an iterative primal-dual solver for nonconvex equality-constrained quadratic optimization subproblems. The solver constructs the primal and dual trial steps from the subspace generated by the generalized Arnoldi procedure used in flexible GMRES (FGMRES). This permits the use of a wide range of preconditioners for the primal-dual system. In contrast with FGMRES, the proposed … Read more

    Gas Network Optimization: A comparison of Piecewise Linear Models

  • Carlos M. Correa-Posada
  • Pedro Sanchez-Martan
    • Categories (Mixed) Integer Linear Programming, Chemical Engineering Tags , , , , ,

    Gas network optimization manages the gas transport by minimizing operating costs and fulfilling contracts between consumers and suppliers. This is an NP- hard problem governed by non-convex and nonlinear gas transport functions that can be modeled by mixed integer linear programming (MILP) techniques. Under these methods, piecewise linear functions describe nonlinearities and bi- nary variables … Read more

    Optimal scheduling for replacing perimeter guarding unmanned aerial vehicles

  • Oleg Burdakov
  • Patrick Doherty
  • Jonas Kvarnström
    • Categories Civil and Environmental Engineering, Global Optimization, Scheduling

    Guarding the perimeter of an area in order to detect potential intruders is an important task in a variety of security-related applications. This task can in many circumstances be performed by a set of camera-equipped unmanned aerial vehicles (UAVs). Such UAVs will occasionally require refueling or recharging, in which case they must temporarily be replaced … Read more