Fundamentals of Convex Analysis

By J. Hiriart-Urruty, Claude Lemaréchal. 2004

737 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/e820a224d0f55a7bdae9ed2034a5efd8ae44fc13

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In Applied Mathematics

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Citations in the corpus

Monotone stability of quadratic semimartingales with applications to unbounded general quadratic BSDEs (2011, methodology): “ROUI In this lemma, the various functions are regularized through the Lipschitzian regularization, whist the function κn is the Moreau–Yoshida regularization of bn (see Hiriart-Urruty and Lemar´echal [23], Chapter E, for more details). Existence result. The important point now is to prove that the s”
Efficient Output Kernel Learning for Multiple Tasks (2015, positive): “Note that as φ is a proper, lower semi-continuous convex function it holds [27, Corollary 1.4.4] Θ rs ∈ ∂φ ∗ ( ρ rs ) ⇐⇒ ρ rs ∈ ∂φ (Θ rs ) .”
Iteration complexity of feasible descent methods for convex optimization (2014, background): “Proof The proof is modified from Hiriart-Urruty and Lemaréchal (2001) Proposition 3.”
Constrained 1-Spectral Clustering (2012, background): “nvex and positively onehomogeneous function.2 Moreover, every even, convex positively one-homogeneous function, T: RV !R has the form T(f) = sup u2U hu;fi, where Uis a symmetric convex set, see e.g., [10]. Note that S(1) = 0 and thus because of the symmetry of Uit has to hold hu;1i= 0 for all u2U. S”
Convex Optimization in Normed Spaces (2015, background): “The exposition in [64] is deep, well-written and rich in geometric insight (see also [26]).”
Iterative algorithm with self-adaptive step size for approximating the common solution of variational inequality and fixed point problems (2021, background): “We say that c is subdifferentiable on H if c is subdifferentiable at each x ∈ H [40].”
A Passivity-Based Approach to Nash Equilibrium Seeking Over Networks (2017, methodology): “The polar cone of a convex cone C is given by Lemma 1 (Moreau’s Decomposition Theorem III.3.2.5, [25]) .”
Optimal investment with random endowments in incomplete markets (2004, neutral): “in [18].”
Information, Divergence and Risk for Binary Experiments (2009, methodology): “When φ(s) is a function of a real argument s and the derivative φ′(s) exists, the Legendre-Fenchel conjugate φ? is given by the Legendre transform (Hiriart-Urruty and Lemaréchal, 2001; Rockafellar, 1970)”
Performance Bounds for Bidirectional Coded Cooperation Protocols (2008, background): “[3] G.”