Aaron Zoll

Inexactly Smooth Performance Estimation and New Optimized Gradient Methods

  • Aaron Zoll
  • Benjamin Grimmer
    • Categories Convex Optimization, Nonlinear Optimization, Nonsmooth Optimization Tags , , ,

      We consider a general class of “inexactly smooth” convex functions, providing a universal model capturing as special cases $L$-smooth, $M$-Lipschitz, and H\”older smooth functions, and any combination thereof. Such functions possess a calculus closely following that of smooth functions. Our main results provide inexactly smooth functions with interpolation theorems that are necessary and sufficient … Read more

    A Universally Optimal Primal-Dual Method for Minimizing Heterogeneous Compositions

  • Aaron Zoll
  • Benjamin Grimmer
    • Categories Constrained Nonlinear Optimization, Convex Optimization, Nonsmooth Optimization Tags , , , ,

    This paper proposes a universal, optimal algorithm for convex minimization problems of the composite form $g_0(x)+h(g_1(x),\dots, g_m(x)) + u(x)$. We allow each $g_j$ to independently range from being nonsmooth Lipschitz to smooth, from convex to strongly convex, described by notions of H\”older continuous gradients and uniform convexity. Note that, although the objective is built from … Read more