Basic Sciences Applications

Economic Impacts of Advanced Weather Forecasting on Energy System Operations

  • Mihai Anitescu
  • Emil M. Constantinescu
  • Victor M. Zavala
    • Categories Basic Sciences Applications, Statistics, Stochastic Programming

    We analyze the impacts of adopting advanced weather forecasting systems at different levels of the decision-making hierarchy of the power grid. Using case studies, we show that state-of-the-art numerical weather prediction (NWP) models can provide high-precision forecasts and uncertainty information that can significantly enhance the performance of planning, scheduling, energy management, and feedback control systems. … Read more

    On Low Rank Matrix Approximations with Applications to Synthesis Problem in Compressed Sensing

  • Anatoli Juditsky
  • Fatma Kılınç-Karzan
  • Arkadi Nemirovski
    • Categories Basic Sciences Applications, Stochastic Programming Tags ,

    We consider the synthesis problem of Compressed Sensing: given $s$ and an $M\times n$ matrix $A$, extract from $A$ an $m\times n$ submatrix $A_m$, with $m$ as small as possible, which is $s$-good, that is, every signal $x$ with at most $s$ nonzero entries can be recovered from observation $A_m x$ by $\ell_1$ minimization: $x … Read more

    On the nonexistence of sum of squares certificates for the BMV conjecture

  • Kristijan Cafuta
  • Igor Klep
  • Janez Povh
    • Categories Basic Sciences Applications, Semi-definite Programming Tags , , , , ,

    The algebraic reformulation of the BMV conjecture is equivalent to a family of dimensionfree tracial inequalities involving positive semidefinite matrices. Sufficient conditions for these to hold in the form of algebraic identities involving polynomials in noncommuting variables have been given by Markus Schweighofer and the second author. Later the existence of these certificates has been … Read more

    Analysis and Generalizations of the Linearized Bregman Method

  • Wotao Yin
    • Categories Basic Sciences Applications, Convex Optimization Tags , , , ,

    This paper reviews the Bregman methods, analyzes the linearized Bregman method, and proposes fast generalization of the latter for solving the basis pursuit and related problems. The analysis shows that the linearized Bregman method has the exact penalty property, namely, it converges to an exact solution of the basis pursuit problem if and only if … Read more

    Fast Generation of Potentials for Self-Assembly of Particles

  • Sorin Costiner
  • Philip du Toit
  • Katalin Grubits
  • Jerrold Marsden
    • Categories Basic Sciences Applications Tags ,

    We address the inverse problem of designing isotropic pairwise particle interaction potentials that lead to the formation of a desired lattice when a system of particles is cooled. The design problem is motivated by the desire to produce materials with pre-specified structure and properties. We present a heuristic computation-free geometric method, as well as a … Read more

    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

    Duality-Based Algorithms for Total-Variation-Regularized Image Restoration

  • Tony F. Chan
  • Stephen Wright
  • Mingqiang Zhu
    • Categories Basic Sciences Applications, Convex Optimization Tags , ,

    Image restoration models based on total variation (TV) have become popular since their introduction by Rudin, Osher, and Fatemi (ROF) in 1992. The dual formulation of this model has a quadratic objective with separable constraints, making projections onto the feasible set easy to compute. This paper proposes application of gradient projection (GP) algorithms to the … Read more

    A Linear Programming Approach for the Least-Squares Protein Morphing Problem

  • Mihai Anitescu
  • Sanghyun Park
    • Categories Approximation Algorithms, Basic Sciences Applications, Linear Programming Tags , , , ,

    This work addresses the computation of free-energy di fferences between protein conformations by using morphing (i.e., transformation) of a source conformation into a target conformation. To enhance the morph- ing procedure, we employ permutations of atoms; we transform atom n in the source conformation into atom \sigma(n) in the target conformation rather than directly transforming atom … Read more

    An SDP-based divide-and-conquer algorithm for large scale noisy anchor-free graph realization

  • Ngai-Hang Z. Leung
  • Kim-Chuan Toh
    • Categories Basic Sciences Applications, Global Optimization Applications, Semi-definite Programming Tags , , ,

    We propose the DISCO algorithm for graph realization in $\real^d$, given sparse and noisy short-range inter-vertex distances as inputs. Our divide-and-conquer algorithm works as follows. When a group has a sufficiently small number of vertices, the basis step is to form a graph realization by solving a semidefinite program. The recursive step is to break … Read more

    The N – k Problem in Power Grids: New Models, Formulations and Computation

  • Daniel Bienstock
  • Abhinav Verma
    • Categories Basic Sciences Applications, Integer Programming, Polyhedra Tags ,

    Given a power grid modeled by a network together with equations describing the power flows, power generation and consumption, and the laws of physics, the so-called N – k problem asks whether there exists a set of k or fewer arcs whose removal will cause the system to fail. We present theoretical results and computation … Read more