hankel matrix

Forecasting Urban Traffic States with Sparse Data Using Hankel Temporal Matrix Factorization

  • Chun Cheng
    • Categories Data Science Algorithms, Data Science Applications, Transportation Tags , , , ,

    Forecasting urban traffic states is crucial to transportation network monitoring and management, playing an important role in the decision-making process. Despite the substantial progress that has been made in developing accurate, efficient, and reliable algorithms for traffic forecasting, most existing approaches fail to handle sparsity, high-dimensionality, and nonstationarity in traffic time series and seldom consider … Read more

    Minimizer extraction in polynomial optimization is robust

  • Igor Klep
  • Janez Povh
  • Jurij Volčič
    • Categories Semi-definite Programming Tags , , , , , , , ,

    In this article we present a robustness analysis of the extraction of optimizers in polynomial optimization. Optimizers can be extracted by solving moment problems using flatness and the Gelfand-Naimark-Segal (GNS) construction. Here a modification of the GNS construction is presented that applies even to non-flat data, and then its sensitivity under perturbations is studied. The … Read more

    Constrained trace-optimization of polynomials in freely noncommuting variables

  • Igor Klep
  • Janez Povh
    • Categories Basic Sciences Applications, Constrained Nonlinear Optimization, Semi-definite Programming Tags , , , , , , , , ,

    The study of matrix inequalities in a dimension-free setting is in the realm of free real algebraic geometry (RAG). In this paper we investigate constrained trace and eigenvalue optimization of noncommutative polynomials. We present Lasserre’s relaxation scheme for trace optimization based on semidefinite programming (SDP) and demonstrate its convergence properties. Finite convergence of this relaxation … Read more

    Hankel Matrix Rank Minimization with Applications to System Identification and Realization

  • Maryam Fazel
  • Ting Kei Pong
  • Defeng Sun
  • Paul Tseng
    • Categories Applications - Science and Engineering, Convex and Nonsmooth Optimization, Linear, Cone and Semidefinite Programming Tags , , , , ,

    We introduce a flexible optimization framework for nuclear norm minimization of matrices with linear structure, including Hankel, Toeplitz and moment structures, and catalog applications from diverse fields under this framework. We discuss various first-order methods for solving the resulting optimization problem, including alternating direction methods of multipliers, proximal point algorithms and gradient projection methods. We … Read more