3 ms·

i havent heard of clarke gradient before. convex analysis has something called subgradient [0], is it different? [0] https://en.m.wikipedia.org/wiki/Subderivat

• ogogmad 5y ago
  The subgradient in convex analysis is a special case of the Clarke gradient. The subgradient is precisely the Clarke gradient for convex functions. Convex functions are always locally Lipschitz except in weird cases. [edit] Question: Are there numerical applications in which the subgradient is actually computed, or is it a purely analytical tool?
  • agnosticmantis 5y ago
    (Stochastic) subgradient methods are used in practice to optimize non-differentiable convex functions. They have a slower convergence rate than (stochastic) gradient descent though. See for example : https://www.stat.cmu.edu/~ryantibs/convexopt-F15/lectures/07-sg-method.pdf https://www.stat.cmu.edu/~ryantibs/convexopt-F15/lectures/07...
  • fault1 5y ago
    yes, see: https://juliadiff.org/ChainRulesCore.jl/dev/maths/nondiff_points.html https://juliadiff.org/ChainRulesCore.jl/dev/maths/nondiff_po... and related neat usages in set based optimization methods in MathOptInterface (part of JuMP.jl): https://matbesancon.xyz/post/2020-12-24-chains_sets2/ https://matbesancon.xyz/post/2020-12-24-chains_sets2/
    • ogogmad 5y ago
      To me, it looks like you're computing a single element from the set, instead of the whole set. Which makes sense, but it's an important caveat.