It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given.
It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given ...
It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given ...
It is shown that Lipschitzian functions are strictly convex if and only if their generalized gradients are disjoint at distinct interior points of a given ...
The equivalence of strict convexity and injectivity of the gradient in bounded level sets. Griewank, Andreas; Jongen, Hubertus Th.; Kwong, Man Kam.
The equivalence of strict convexity and injectivity of the gradient in bounded level sets. Griewank, Andreas (Author) ; Jongen, Hubertus Th. (Author) ; Kwong ...
The equivalence of strict convexity and injectivity of the gradient in bounded level sets · A. GriewankH. JongenM. Kwong. Mathematics. Math. Program. 1991. It ...
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Strong convexity ⇒ Strict convexity ⇒ Convexity. (But the converse of neither implication is true.) Proof: The fact that strict convexity implies convexity is ...
Missing: injectivity | Show results with:injectivity
The level sets of the norm of a convex function's gradient
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Oct 29, 2024 · Take f(x,y)=45(|x|5/4+|y|5/4),. with ∇f=(x1/4y1/4). and ‖∇f‖22=|x|1/2+|y|1/2,. so that {(x,y): ‖∇f‖22≤c2} is non-convex for all c>0.
Missing: convexity injectivity
The Gradient Inequality for Strictly Convex Functions. Proposition Let f : C → R be a continuously differentiable function defined on a convex set C ⊆ Rn.