averaging

Expected Value of Matrix Quadratic Forms with Wishart distributed Random Matrices

  • Melinda Hagedorn
    • Categories Convex Optimization, Data Science Theory, Stochastic Approaches Tags , , , , ,

    To explore the limits of a stochastic gradient method, it may be useful to consider an example consisting of an infinite number of quadratic functions. In this context, it is appropriate to determine the expected value and the covariance matrix of the stochastic noise, i.e. the difference of the true gradient and the approximated gradient … Read more

    Approximate Primal Solutions and Rate Analysis in Dual Subgradient Methods

  • Angelia Nedich
  • Asuman Ozdaglar
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    We study primal solutions obtained as a by-product of subgradient methods when solving the Lagrangian dual of a primal convex constrained optimization problem (possibly nonsmooth). The existing literature on the use of subgradient methods for generating primal optimal solutions is limited to the methods producing such solutions only asymptotically (i.e., in the limit as the … Read more