gauss-seidel

Analyzing Random Permutations for Cyclic Coordinate Descent

  • Stephen Wright
  • Ching-pei Lee
    • Categories Unconstrained Optimization Tags , , ,

    We consider coordinate descent methods on convex quadratic problems, in which exact line searches are performed at each iteration. (This algorithm is identical to Gauss-Seidel on the equivalent symmetric positive definite linear system.) We describe a class of convex quadratic problems for which the random-permutations version of cyclic coordinate descent (RPCD) outperforms the standard cyclic … Read more

    Bridging the Gap Between Multigrid, Hierarchical, and Receding-Horizon Control

  • Victor M. Zavala
    • Categories Distributed Control, Nonlinear Optimization, Systems governed by Differential Equations Optimization Tags , , , ,

    We analyze the structure of the Euler-Lagrange conditions of a lifted long-horizon optimal control problem. The analysis reveals that the conditions can be solved by using block Gauss-Seidel schemes and we prove that such schemes can be implemented by solving sequences of short-horizon problems. The analysis also reveals that a receding-horizon control scheme is equivalent … Read more