optimal diagonal preconditioner

Searching for Optimal Per-Coordinate Step-sizes with Multidimensional Backtracking

  • Frederik Kunstner
  • Mark Schmidt
    • Categories Convex Optimization, Nonlinear Optimization Tags , ,

    The backtracking line-search is an effective technique to automatically tune the step-size in smooth optimization. It guarantees similar performance to using the theoretically optimal step-size. Many approaches have been developed to instead tune per-coordinate step-sizes, also known as diagonal preconditioners, but none of the existing methods are provably competitive with the optimal per-coordinate stepsizes. We … Read more

    Simple Efficient Solutions for Semidefinite Programming

  • Henry Wolkowicz
    • Categories Combinatorial Optimization, Nonlinear Systems and Least-Squares, Semi-definite Programming Tags , , , , ,

    This paper provides a simple approach for solving a semidefinite program, SDP\@. As is common with many other approaches, we apply a primal-dual method that uses the perturbed optimality equations for SDP, $F_\mu(X,y,Z)=0$, where $X,Z$ are $n \times n$ symmetric matrices and $y \in \Re^n$. However, we look at this as an overdetermined system of … Read more