Robert Michael Lewis

Automatically Assessing the Performance of an Optimization-Based Multigrid Method

  • Robert Michael Lewis
  • Stephen G. Nash
    • Categories Systems governed by Differential Equations Optimization Tags , ,

    Many large nonlinear optimization problems are based upon discretizations of underlying function spaces. Optimization-based multigrid methods—that is, multigrid methods based on solving coarser versions of an optimization problem—are designed to solve such discretized problems efficiently by taking explicit advantage of the family of discretizations. The methods are generalizations of more traditional multigrid methods for solving … Read more

    Asynchronous parallel generating set search for linearly-constrained optimization

  • Joshua D. Griffin
  • Robert Michael Lewis
  • Tamara Kolda
    • Categories Constrained Nonlinear Optimization, Parallel Algorithms, Robust Optimization Tags , , , , , , , ,

    Generating set search (GSS) is a family of direct search methods that encompasses generalized pattern search and related methods. We describe an algorithm for asynchronous linearly-constrained GSS, which has some complexities that make it different from both the asynchronous bound-constrained case as well as the synchronous linearly-constrained case. The algorithm has been implemented in the … Read more

    Model Problems for the Multigrid Optimization of Systems Governed by Differential Equations

  • Robert Michael Lewis
  • Stephen G. Nash
    • Categories Infinite Dimensional Optimization, Optimization of Systems modeled by PDEs, Systems governed by Differential Equations Optimization Tags ,

    We present a multigrid approach to the optimization of systems governed by differential equations. Such optimization problems have many applications, and are a broader class of problems than systems of equations. Using several model problems we give evidence (both theoretical and numerical) that a multigrid approach can often be successful in the setting of optimization. … Read more