A. Numerical Computation

  • Numeric / continuous
    • Computation of a subgradient (the whole subdifferential?)
    • Computation of the convex enveloppe.
    • Computation of the dual(polar) set of a 2- 3- dimensional convex set.
  • Numeric / Discrete
    • Set operations for polytopes: internal/external representation, union, intersection, dual, convex hull, extreme points...
    • All functional operations for piecewise affine functions ( inf-convolution).
  • Approximation of a convex set by polytopes and of a convex function by a piecewise affine function.
A (lower) convex hull
A (lower) convex hull

B. Symbolic Computation

  • Functions on the real-line:
    • Test for convexity: positive definiteness of the Hessian...
    • Test for lower semi-continuity
  • Functions in a low-dimensional space (less than 5 dimensions)
    • Conjugate and biconjugate calculus.
    • Inf-convolution, deconvolution calculus (Moreau-Yosida approximate, Lipschitzian regularization).
    • Subdifferential calculus (at least for elementary convex functions).
    • Tests for convexity.

Yves Lucet Last modified: 05/18/99