What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications

DOI10.1137/080719613zbMath1186.65081OpenAlexW2038690792MaRDI QIDQ5189558

Yves Lucet

Publication date: 17 March 2010

Published in: SIAM Journal on Optimization (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/c8762faac0dbbf6e21e55f31a748e78243033279

zbMATH Keywords

image processingfast Fourier transformHamilton-Jacobi equationsmultifractal analysismax-plus algebraconvex analysisconvex envelopemathematical morphologysurvey articleinf-convolutionLegendre-Fenchel transformMoreau envelopeFenchel conjugatesymbolic-numeric algorithmsdistance transformfast transformsLax-Hopf formulapiecewise linear-quadratic

Mathematics Subject Classification ID

Numerical optimization and variational techniques (65K10) Linear-quadratic optimal control problems (49N10) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming (90-02) Existence theories for problems in abstract spaces (49J27) Research exposition (monographs, survey articles) pertaining to calculus of variations and optimal control (49-02) Numerical approximation and computational geometry (primarily algorithms) (65D99)

Related Items (11)

Graph-Matrix Calculus for Computational Convex Analysis ⋮ Compensated Convexity Methods for Approximations and Interpolations of Sampled Functions in Euclidean Spaces: Theoretical Foundations ⋮ Structure of shocks in Burgers turbulence with Lévy noise initial data ⋮ Convexity conditions and the Legendre-fenchel transform for the product of finitely many positive definite quadratic forms ⋮ Convex hull algorithms for piecewise linear-quadratic functions in computational convex analysis ⋮ Convexity of the proximal average ⋮ Lipschitz minorants of Brownian motion and Lévy processes ⋮ Compensated convexity on bounded domains, mixed Moreau envelopes and computational methods ⋮ The \(\varepsilon\)-strategy in variational analysis: illustration with the closed convexification of a function ⋮ Duality and Convex Programming ⋮ Compensated convexity and Hausdorff stable extraction of intersections for smooth manifolds

This page was built for publication: What Shape Is Your Conjugate? A Survey of Computational Convex Analysis and Its Applications