Estimating Tangent and Normal Cones Without Calculus
Mathematics of Operations Research
Spectral radius minimization for optimal average consensus and output feedback stabilization
Automatica (Journal of IFAC)
Cutting-set methods for robust convex optimization with pessimizing oracles
Optimization Methods & Software
A Nonderivative Version of the Gradient Sampling Algorithm for Nonsmooth Nonconvex Optimization
SIAM Journal on Optimization
A derivative-free approximate gradient sampling algorithm for finite minimax problems
Computational Optimization and Applications
The Clarke Generalized Gradient for Functions Whose Epigraph Has Positive Reach
Mathematics of Operations Research
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Many interesting real functions on Euclidean space are differentiable almost everywhere. All Lipschitz functions have this property, but so, for example, does the spectral abscissa of a matrix (a non-Lipschitz function). In practice, the gradient is often easy to compute. We investigate to what extent we can approximate the Clarke subdifferential of such a function at some point by calculating the convex hull of some gradients sampled at random nearby points.