frank-wolfe

Linear convergence of a modified Frank-Wolfe algorithm for computing minimum volume ellipsoids

  • Selin Damla Ahipasaoglu
  • Peng Sun
  • Michael J. Todd
    • Categories Convex Optimization Tags , , ,

    We show the linear convergence of a simple first-order algorithm for the minimum-volume enclosing ellipsoid problem and its dual, the D-optimal design problem of statistics. Computational tests confirm the attractive features of this method. CitationOptimization Methods and Software 23 (2008), 5–19. ArticleDownload View PDF

    Set Intersection Theorems and Existence of Optimal Solutions

  • Dimitri Bertsekas
  • Paul Tseng
    • Categories Constrained Nonlinear Optimization, Convex Optimization Tags , , ,

    The question of nonemptiness of the intersection of a nested sequence of closed sets is fundamental in a number of important optimization topics, including the existence of optimal solutions, the validity of the minimax inequality in zero sum games, and the absence of a duality gap in constrained optimization. We introduce the new notion of … Read more