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Subdifferential - equivalent definitions?

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#real-analysis #functional-analysis #convex-analysis #non-smooth-analysis
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Optimality check for non-differentiable convex function

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#optimization #convex-analysis #subgradient #non-smooth-analysis #non-smooth-optimization
117
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Subgradient of the spectral norm

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#matrices #matrix-norms #subgradient #spectral-norm #non-smooth-analysis
67
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Subdifferential and affine transformation

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#real-analysis #convex-analysis #subgradient #non-smooth-analysis
33
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Time derivative a nonsmooth convex function. Chain rule.

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#convex-analysis #chain-rule #function-and-relation-composition #non-smooth-analysis
62
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Proof of Theorem 6.14 in "Variational analysis (Rockafellar, Wets)"

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#chain-rule #constraints #variational-analysis #non-smooth-analysis
141
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Fundamental Theorem of Calculus for non-differentiable convex functions

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#real-analysis #reference-request #convex-analysis #subgradient #non-smooth-analysis
76
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For a Lipschitz function, is the gradient (when defined) orthogonal to level set?

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#real-analysis #calculus #multivariable-calculus #vectors #non-smooth-analysis
115
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Is a single-valued (convex) subdifferential sufficient to show differentiability?

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#real-analysis #derivatives #convex-analysis #non-smooth-analysis
95
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The tangent cone at a interior point

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#functional-analysis #non-smooth-analysis
51
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The equivalent definition of tangent cone in normed space

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#functional-analysis #non-smooth-analysis
117
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Directional derivative of proximal mapping of a convex function

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#derivatives #convex-analysis #convex-optimization #proximal-operators #non-smooth-analysis
25
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Nonsmooth analysis: Need help clarifying a step in the proof that $co D^\ast u(x) = \partial f(x)$

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#analysis #proof-explanation #convex-analysis #convex-hulls #non-smooth-analysis
90
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Let $f$ be convex, and $g$ be a convex surrogate of $f$. Does a Lipschitz-smooth $g-f$ imply $f$ and $g$ have the same subgradients?

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#convex-analysis #convex-optimization #non-smooth-analysis #non-smooth-optimization
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Subdifferential of convex functions is nonempty

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#convex-analysis #convex-optimization #subgradient #non-smooth-analysis

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