Applications – Science and Engineering

Stochastic and robust optimal operation of energy-efficient building with combined heat and power systems

  • Ping Liu
    • Categories Applications - Science and Engineering, Robust Optimization, Stochastic Programming Tags , ,

    Energy efficiency and renewable energy become more attractive in smart grid. In order to efficiently reduce global energy usage in building energy systems and to improve local environmental sustainability, it is essential to optimize the operation and the performance of combined heat and power (CHP) systems. In addition, intermittent renewable energy and imprecisely predicted customer … Read more

    Convergence rates of moment-sum-of-squares hierarchies for optimal control problems

  • Didier Henrion
  • Colin N. Jones
  • Milan Korda
    • Categories Control Applications, Semi-definite Programming, Systems governed by Differential Equations Optimization Tags , , , ,

    We study the convergence rate of moment-sum-of-squares hierarchies of semidefinite programs for optimal control problems with polynomial data. It is known that these hierarchies generate polynomial under-approximations to the value function of the optimal control problem and that these under-approximations converge in the $L^1$ norm to the value function as their degree $d$ tends to … Read more

    Mixed-Integer Programming for Cycle Detection in Non-reversible Markov Processes

  • Isabel Beckenbach
  • Leon Eifler
  • Ambros Gleixner
  • Andreas Grever
  • Jakob Witzig
  • Konstantin Fackeldey
  • Marcus Weber
    • Categories (Mixed) Integer Linear Programming, Chemical Engineering, Optimization of Simulated Systems

    In this paper, we present a new, optimization-based method to exhibit cyclic behavior in non-reversible stochastic processes. While our method is general, it is strongly motivated by discrete simulations of ordinary differential equations representing non-reversible biological processes, in particular molecular simulations. Here, the discrete time steps of the simulation are often very small compared to … Read more

    A Riemannian conjugate gradient method for optimization on the Stiefel manifold

  • Xiaojing Zhu
    • Categories Applications - Science and Engineering, Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , , , ,

    In this paper we propose a new Riemannian conjugate gradient method for optimization on the Stiefel manifold. We introduce two novel vector transports associated with the retraction constructed by the Cayley transform. Both of them satisfy the Ring-Wirth nonexpansive condition, which is fundamental for convergence analysis of Riemannian conjugate gradient methods, and one of them … Read more

    On max-k-sums

  • Michael J. Todd
    • Categories Basic Sciences Applications, Convex Optimization, Linear, Cone and Semidefinite Programming Tags , , ,

    The max-$k$-sum of a set of real scalars is the maximum sum of a subset of size $k$, or alternatively the sum of the $k$ largest elements. We study two extensions: First, we show how to obtain smooth approximations to functions that are pointwise max-$k$-sums of smooth functions. Second, we discuss how the max-$k$-sum can … Read more

    Branch and Bound based methods to minimize the energy consumed by an electrical vehicle on long travels with slopes

  • Abdelkader Merakeb
  • Frédéric Messine
  • Riadh Omheni
    • Categories Applications - Science and Engineering, Global Optimization Tags , , , , ,

    We consider the problem of minimization of the energy consumed by an electrical vehicle performing quite long travels with slopes. The model we address here, takes into account the electrical and mechanical differential equations of the vehicle. This yields a mixed-integer optimal control problem that can be approximated, using a methodology based on some decomposition … Read more

    Positioning and construction algorithms for a specific absolute positioning magnetic ruler system

  • Aleksandar Mojsic
    • Categories Basic Sciences Applications Tags , , , , , , ,

    Abstract Absolute positioning magnetic rulers are rulers which calculate the distance of the reading head based just on one reading of a magnetic signal. A new absolute positioning magnetic ruler method which is based on rulers with trapezoidal magnetic poles is considered in this paper. On a fixed position of a ruler, the reading head … Read more

    Convex Variational Formulations for Learning Problems

  • Pedro Borges de Melo
    • Categories Data-Mining Tags , , , , , , ,

    Abstract—In this article, we introduce new techniques to solve the nonlinear regression problem and the nonlinear classification problem. Our benchmarks suggest that our method for regression is significantly more effective when compared to classical methods and our method for classification is competitive. Our list of classical methods includes least squares, random forests, decision trees, boosted … Read more

    Optimization Methods for Locating Heteroclinic Orbits

  • Pedro Borges de Melo
    • Categories Applications - Science and Engineering Tags , ,

    Assume we are given a system of ordinary differential equations x 0 = f(x, p) depending on a parameter p ∈ R pe . In this dissertation we consider the problem of locating a parameter p and an initial condition ξ that give rise to a heteroclinic orbit. In the case that such p and … Read more

    Constructing New Weighted l1-Algorithms for the Sparsest Points of Polyhedral Sets

  • Zhi-Quan Luo
  • Yun-Bin Zhao
    • Categories Basic Sciences Applications, Convex and Nonsmooth Optimization Tags , , , , , ,

    The l0-minimization problem that seeks the sparsest point of a polyhedral set is a longstanding challenging problem in the fields of signal and image processing, numerical linear algebra and mathematical optimization. The weighted l1-method is one of the most plausible methods for solving this problem. In this paper, we develop a new weighted l1-method through … Read more