Relevant bibliographies by topics / Semiconvex functions

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  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters

Academic literature on the topic 'Semiconvex functions'

Author: Grafiati
Published: 1 June 2024
Last updated: 31 July 2025

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Journal articles on the topic "Semiconvex functions"

1

Ngai, Van Huynh, and Jean-Paul Penot. "The Semiconvex Regularization of Functions." SIAM Journal on Optimization 33, no. 3 (2023): 2457–83. http://dx.doi.org/10.1137/22m1496426.

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Zhang, K. "On various semiconvex relaxations of the squared-distance function." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 129, no. 6 (1999): 1309–23. http://dx.doi.org/10.1017/s0308210500019405.

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For the Euclidean squared-distance functionf(·) = dist2(·, K), withK ⊂ MN×n, we show thatKis convex if and only iff(·)equals either its rank-one convex, quasiconvex or polyconvex relaxations. We also establish that if (i)Kis compact and contractible or (ii) dimC(K) = k < Nn, Kis convex if and only iffequals one of the semiconvex relaxations when dist2(P, K)is sufficiently large, and for case (i),P ∈MNxn; for case (ii),P ∈ Ek—a k-dimensional plane containingC(K). We also give some estimates of the difference between dist2(P, K)and its semiconvex relaxations. Some possible extensions to more
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Václav, Kryštof, and Zajíček Luděk. "Differences of two semiconvex functions on the real line." Commentationes Mathematicae Universitatis Carolinae 57, no. 1 (2016): 21–37. http://dx.doi.org/10.14712/1213-7243.2015.153.

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Noor, Muhammad, Khalida Noor, and Muhammad Awan. "Hermite-Hadamard inequalities for relative semi-convex functions and applications." Filomat 28, no. 2 (2014): 221–30. http://dx.doi.org/10.2298/fil1402221n.

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In this paper, we prove some Hermite-Hadamard inequalities for the class of relative semiconvex functions. Several special cases are also discussed. Thus it is worth mentioning that our results can be viewed as a generalization of previous results. Some applications to special means are also presented. Ideas and techniques of this paper may inspire further research in various branches of pure and applied sciences.
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Tabor, Jacek, and Józef Tabor. "Extensions of convex and semiconvex functions and intervally thin sets." Journal of Mathematical Analysis and Applications 365, no. 1 (2010): 43–49. http://dx.doi.org/10.1016/j.jmaa.2009.09.038.

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Colesanti, Andrea, and Paolo Salani. "Generalised solutions of Hessian equations." Bulletin of the Australian Mathematical Society 56, no. 3 (1997): 459–66. http://dx.doi.org/10.1017/s0004972700031257.

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We introduce a definition of generalised solutions of the Hessian equation Sm(D2u) = f in a convex set ω ⊂ ℝn, where Sm(D2u) denotes the m-th symmetric function of the eigenvalues of D2u, f ∈ Lp(ω), p ≥ 1, and m ∈ {1, …, n}. Such a definition is given in the class of semi-convex functions, and it extends the definition of convex generalised solutions for the Monge-Ampère equation. We prove that semiconvex weak solutions are solutions in the sense of the present paper.
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Sturm, Karl-Theodor. "Gradient flows for semiconvex functions on metric measure spaces – existence, uniqueness, and Lipschitz continuity." Proceedings of the American Mathematical Society 146, no. 9 (2018): 3985–94. http://dx.doi.org/10.1090/proc/14061.

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Chen, Ping, and Wing-Sum Cheung. "Hermite–Hadamard inequality for semiconvex functions of rate $(k_1,k_2)$ on the coordinates and optimal mass transportation." Rocky Mountain Journal of Mathematics 50, no. 6 (2020): 2011–21. http://dx.doi.org/10.1216/rmj.2020.50.2011.

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Braga, J. Ederson M., Alessio Figalli, and Diego Moreira. "Optimal Regularity for the Convex Envelope and Semiconvex Functions Related to Supersolutions of Fully Nonlinear Elliptic Equations." Communications in Mathematical Physics 367, no. 1 (2019): 1–32. http://dx.doi.org/10.1007/s00220-019-03370-2.

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Dower, Peter M. "Coverage control and function approximation via semiconcave and semiconvex duality." Mathematics of Control, Signals, and Systems, March 20, 2025. https://doi.org/10.1007/s00498-025-00411-1.

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Abstract A min-of-quadratics representation for the cost function underlying a popular approach to classical coverage control is used to motivate and develop connections to function approximation via semiconcave and semiconvex duality. By considering functions that are both semiconcave and semiconvex, upper and lower bounds are developed via their semiconcave and semiconvex relaxations. Min-of-quadratics and max-of-quadratics representations for these bounds are provided by construction, using quadratic basis functions that are synonymous with agents. These representations induce a pair of Vor
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Dissertations / Theses on the topic "Semiconvex functions"

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Jerhaoui, Othmane. "Viscosity theory of first order Hamilton Jacobi equations in some metric spaces." Electronic Thesis or Diss., Institut polytechnique de Paris, 2022. http://www.theses.fr/2022IPPAE016.

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La première partie de cette thèse est consacrée à l'étude d'une équation de Hamilton Jacobi Bellman discontinue, définie sur une stratification de R^N. Cette dernière est le résultat d'une union d'une collection finie de sous-variétés lisses et disjointes de R^N, que l'on nomme les sous-domaines. Sur chaque sous-domaine, un Hamiltonien continue y est définie. Cependant, le Hamiltonien global sur R^N présente des discontinuités lorsque l'on passe d'un sous-domaine à l'autre. On donne une interprétation commande optimale de ce problème et on utilise les techniques de l'analyse non lisse pour mon
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Mazade, Marc. "Ensembles localement prox-réguliers et inéquations variationnelles." Thesis, Montpellier 2, 2011. http://www.theses.fr/2011MON20141.

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Les propriétés des ensembles localement prox-réguliers ont été étudiées par R.A. Poliquin, R.T. Rockafellar et L. Thibault. Le concept de fonction ''primal lower nice'' a été introduit en dimension finie par R.A. Poliquin et étendu au cadre Hilbertien par A.B. Levy, R.A. Poliquin et L. Thibault. Dans cette thèse, la première partie est consacrée à une étude des outils et des objets géométriques de l'Analyse non lisse tels que les fonctions primal lower nice et les ensembles localement prox-réguliers. On donnera une définition quantifiée de la prox-régularité locale. La deuxième partie établit
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Book chapters on the topic "Semiconvex functions"

1

"Semiconvex functions." In Unilateral Variational Analysis in Banach Spaces. WORLD SCIENTIFIC, 2023. http://dx.doi.org/10.1142/9789811258176_0010.

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