Applications – Science and Engineering

Convergent relaxations of polynomial optimization problems with non-commuting variables

  • Antonio Acin
  • Miguel Navascues
  • Stefano Pironio
    • Categories Basic Sciences Applications, Linear, Cone and Semidefinite Programming Tags , , ,

    We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalities as semidefinite positivity constraints. Such problems arise naturally in quantum theory and quantum information science. To solve them, we introduce a hierarchy … Read more

    Provably Near-Optimal Solutions for Very Large Single-Row Facility Layout Problems

  • Miguel F. Anjos
  • Ginger Yen
    • Categories Applications - Science and Engineering, Global Optimization, Semi-definite Programming Tags , , , ,

    The facility layout problem is a global optimization problem that seeks to arrange a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. This paper is concerned with the single-row facility layout problem (SRFLP), the one-dimensional version of facility layout that is also … Read more

    Classification with Guaranteed Probability of Error

  • Marco C. Campi
    • Categories Data-Mining, Semi-definite Programming, Statistics Tags , , , ,

    We introduce a general-purpose learning machine that we call the “Guaranteed Error Machine”, or GEM, and two learning algorithms, a “real GEM algorithm” and an “ideal GEM algorithm”. The real GEM algorithm is for use in real applications, while the ideal GEM algorithm is introduced as a theoretical tool; however, these two algorithms have identical … Read more

    On-Line Economic Optimization of Energy Systems Using Weather Forecast Information

  • Mihai Anitescu
  • Emil M. Constantinescu
  • Victor M. Zavala
  • Theodore Krause
    • Categories Chemical Engineering, Control Applications, Stochastic Programming Tags , , , , ,

    We establish an on-line optimization framework to exploit weather forecast information in the operation of energy systems. We argue that anticipating the weather conditions can lead to more proactive and cost-effective operations. The framework is based on the solution of a stochastic dynamic real-time optimization (D-RTO) problem incorporating forecasts generated from a state-of-the-art weather prediction … Read more

    An Interior-Point Algorithm for Large-Scale Nonlinear Optimization with Inexact Step Computations

  • Frank E. Curtis
  • Olaf Schenk
    • Categories Nonlinear Optimization, Optimization of Systems modeled by PDEs Tags , , , , , ,

    We present a line-search algorithm for large-scale continuous optimization. The algorithm is matrix-free in that it does not require the factorization of derivative matrices. Instead, it uses iterative linear system solvers. Inexact step computations are supported in order to save computational expense during each iteration. The algorithm is an interior-point approach derived from an inexact … Read more

    High accuracy semidefinite programming bounds for kissing numbers

  • Hans D Mittelmann
  • Frank Vallentin
    • Categories Applications - Science and Engineering, Linear, Cone and Semidefinite Programming, Semi-definite Programming Tags , , ,

    The kissing number in n-dimensional Euclidean space is the maximal number of non-overlapping unit spheres which simultaneously can touch a central unit sphere. Bachoc and Vallentin developed a method to find upper bounds for the kissing number based on semidefinite programming. This paper is a report on high accuracy calculations of these upper bounds for … Read more

    An interior-point Lagrangian decomposition method for separable convex optimization

  • Ion Necoara
  • Johan Suykens
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , ,

    In this paper we propose a distributed algorithm for solving large-scale separable convex problems using Lagrangian dual decomposition and the interior-point framework. By adding self-concordant barrier terms to the ordinary Lagrangian we prove under mild assumptions that the corresponding family of augmented dual functions is self-concordant. This makes it possible to efficiently use the Newton … Read more

    Application of a smoothing technique to decomposition in convex optimization

  • Ion Necoara
  • Johan Suykens
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization Tags , , , ,

    Dual decomposition is a powerful technique for deriving decomposition schemes for convex optimization problems with specific structure. Although the Augmented Lagrangian is computationally more stable than the ordinary Lagrangian, the \textit{prox-term} destroys the separability of the given problem. In this paper we use another approach to obtain a smooth Lagrangian, based on a smoothing technique … Read more

    A Fast Moving Horizon Estimation Algorithm Based on Nonlinear Programming Sensitivity

  • Lorenz T. Biegler
  • Carl D. Laird
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    Moving Horizon Estimation (MHE) is an efficient optimization-based strategy for state estimation. Despite the attractiveness of this method, its application in industrial settings has been rather limited. This has been mainly due to the difficulty to solve, in real-time, the associated dynamic optimization problems. In this work, a fast MHE algorithm able to overcome this … Read more

    The Advanced Step NMPC Controller: Optimality, Stability and Robustness

  • Lorenz T. Biegler
  • Victor M. Zavala
    • Categories Control Applications, Nonlinear Optimization, Optimization of Systems modeled by PDEs

    Widespread application of dynamic optimization with fast optimization solvers leads to increased consideration of first-principles models for nonlinear model predictive control (NMPC). However, significant barriers to this optimization-based control strategy are feedback delays and consequent loss of performance and stability due to on-line computation. To overcome these barriers, recently proposed NMPC controllers based on nonlinear … Read more