performance estimation problems

Performance Estimation for Smooth and Strongly Convex Sets

  • Alan Luner
  • Benjamin Grimmer
    • Categories Convex Optimization, Semi-definite Programming Tags , , , , ,

    We extend recent computer-assisted design and analysis techniques for first-order optimization over structured functions–known as performance estimation–to apply to structured sets. We prove “interpolation theorems” for smooth and strongly convex sets with Slater points and bounded diameter, showing a wide range of extremal questions amount to structured mathematical programs. Prior function interpolation theorems are recovered … Read more

    On Averaging and Extrapolation for Gradient Descent

  • Alan Luner
  • Benjamin Grimmer
    • Categories Convex Optimization, Semi-definite Programming Tags , , , ,

    This work considers the effect of averaging, and more generally extrapolation, of the iterates of gradient descent in smooth convex optimization. After running the method, rather than reporting the final iterate, one can report either a convex combination of the iterates (averaging) or a generic combination of the iterates (extrapolation). For several common stepsize sequences, … Read more

    Worst-case convergence analysis of gradient and Newton methods through semidefinite programming performance estimation

  • Etienne de Klerk
  • François Glineur
  • Adrien B. Taylor
    • Categories Linear, Cone and Semidefinite Programming, Nonlinear Optimization Tags , , ,

    We provide new tools for worst-case performance analysis of the gradient (or steepest descent) method of Cauchy for smooth strongly convex functions, and Newton’s method for self-concordant functions. The analysis uses semidefinite programming performance estimation, as pioneered by Drori en Teboulle [Mathematical Programming, 145(1-2):451–482, 2014], and extends recent performance estimation results for the method of … Read more