structure

Accelerated gradient sliding for structured convex optimization

  • Guanghui Lan
  • Yuyuan Ouyang
    • Categories Convex and Nonsmooth Optimization, Nonlinear Optimization Tags , , , ,

    Our main goal in this paper is to show that one can skip gradient computations for gradient descent type methods applied to certain structured convex programming (CP) problems. To this end, we first present an accelerated gradient sliding (AGS) method for minimizing the summation of two smooth convex functions with different Lipschitz constants. We show … Read more

    Multi-Secant Equations, Approximate Invariant Subspaces and Multigrid Optimization

  • Serge Gratton
  • Philippe L. Toint
    • Categories Optimization of Systems modeled by PDEs, Unconstrained Optimization Tags , , ,

    New approximate secant equations are shown to result from the knowledge of (problem dependent) invariant subspace information, which in turn suggests improvements in quasi-Newton methods for unconstrained minimization. It is also shown that this type of information may often be extracted from the multigrid structure of discretized infinite dimensional problems. A new limited-memory BFGS using … Read more