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Volumn 43, Issue 1, 2009, Pages 95-118

The piecewise linear-quadratic model for computational convex analysis

Author keywords

Computational convex analysis; Convex analysis; Fenchel conjugate; Legendre Fenchel transform; Moreau envelope; Moreau Yosida approximate; Proximal average

Indexed keywords

COMPUTATIONAL CONVEX ANALYSIS; CONVEX ANALYSIS; FENCHEL CONJUGATE; LEGENDRE-FENCHEL TRANSFORM; MOREAU ENVELOPE; MOREAU-YOSIDA APPROXIMATE; PROXIMAL AVERAGE;

EID: 67449092643     PISSN: 09266003     EISSN: 15732894     Source Type: Journal    
DOI: 10.1007/s10589-007-9124-y     Document Type: Article
Times cited : (30)

References (40)
  • 2
    • 67449086128 scopus 로고    scopus 로고
    • How to transform one convex function continuously into another
    • University of British Columbia, July 2006. Accepted for publication in SIAM Review
    • Bauschke, H.H., Lucet, Y., Trienis, M.: How to transform one convex function continuously into another. Technical report, University of British Columbia, July 2006. Accepted for publication in SIAM Review
    • Technical report
    • Bauschke, H.H.1    Lucet, Y.2    Trienis, M.3
  • 3
    • 0347269125 scopus 로고    scopus 로고
    • Projection and proximal point methods: Convergence results and counterexamples
    • H.H. Bauschke E. Matoušková S. Reich 2004 Projection and proximal point methods: Convergence results and counterexamples Nonlinear Anal. 56 715 738
    • (2004) Nonlinear Anal. , vol.56 , pp. 715-738
    • Bauschke, H.H.1    E. Matoušková2    Reich, S.3
  • 5
    • 45749111443 scopus 로고    scopus 로고
    • Symbolic Fenchel conjugation
    • 10.1007/s10107-007-0134-4
    • J.M. Borwein C.H. Hamilton 2007 Symbolic Fenchel conjugation Math. Program. 10.1007/s10107-007-0134-4
    • (2007) Math. Program.
    • Borwein, J.M.1    Hamilton, C.H.2
  • 6
    • 0001355283 scopus 로고
    • Un algorithme rapide pour le calcul de transformées de Legendre-Fenchel discrètes
    • Y. Brenier 1989 Un algorithme rapide pour le calcul de transformées de Legendre-Fenchel discrètes C. R. Acad. Sci. Paris Sér. I Math. 308 587 589
    • (1989) C. R. Acad. Sci. Paris Sér. I Math. , vol.308 , pp. 587-589
    • Brenier, Y.1
  • 7
    • 0000759411 scopus 로고    scopus 로고
    • Fast Legendre-Fenchel transform and applications to Hamilton-Jacobi equations and conservation laws
    • L. Corrias 1996 Fast Legendre-Fenchel transform and applications to Hamilton-Jacobi equations and conservation laws SIAM J. Numer. Anal. 33 1534 1558
    • (1996) SIAM J. Numer. Anal. , vol.33 , pp. 1534-1558
    • Corrias, L.1
  • 13
    • 0026123473 scopus 로고
    • On the convergence of the proximal point algorithm for convex minimization
    • O. Güler 1991 On the convergence of the proximal point algorithm for convex minimization SIAM J. Control Optim. 29 403 419
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 403-419
    • O. Güler1
  • 15
    • 66049119555 scopus 로고    scopus 로고
    • Ph.D. thesis, Institut des Sciences de l'Ingenieur de Toulon et du Var, Laboratoire Modélisation Numérique et Couplages, BP 56, 83162 La Valette CEDEX, France, Jan. 2005. Habilitation à Diriger des Recherches
    • Helluy, P.: Simulation numérique des écoulements multiphasiques: de la théorie aux applications. Ph.D. thesis, Institut des Sciences de l'Ingenieur de Toulon et du Var, Laboratoire Modélisation Numérique et Couplages, BP 56, 83162 La Valette CEDEX, France, Jan. 2005. Habilitation à Diriger des Recherches
    • Simulation numérique des écoulements multiphasiques: de la théorie aux applications
    • Helluy, P.1
  • 16
    • 0009631167 scopus 로고
    • Lipschitz r-continuity of the approximate subdifferential of a convex function
    • J.-B. Hiriart-Urruty 1980 Lipschitz r-continuity of the approximate subdifferential of a convex function Math. Scand. 47 123 134
    • (1980) Math. Scand. , vol.47 , pp. 123-134
    • Hiriart-Urruty, J.-B.1
  • 18
    • 34547195180 scopus 로고    scopus 로고
    • Parametric computation of the Legendre-Fenchel conjugate with application to the computation of the Moreau envelope
    • J.-B. Hiriart-Urruty Y. Lucet 2007 Parametric computation of the Legendre-Fenchel conjugate with application to the computation of the Moreau envelope J. Convex Anal. 14 3 657 666
    • (2007) J. Convex Anal. , vol.14 , Issue.3 , pp. 657-666
    • Hiriart-Urruty, J.-B.1    Lucet, Y.2
  • 23
    • 0030197212 scopus 로고    scopus 로고
    • A fast computational algorithm for the Legendre-Fenchel transform
    • Y. Lucet 1996 A fast computational algorithm for the Legendre-Fenchel transform Comput. Optim. Appl. 6 27 57
    • (1996) Computational Optimization and Applications , vol.6 , Issue.1 , pp. 27-57
    • Lucet, Y.1
  • 24
    • 0004879867 scopus 로고    scopus 로고
    • Faster than the Fast Legendre Transform, the linear-time Legendre Transform
    • Y. Lucet 1997 Faster than the fast Legendre transform, the Linear-time Legendre transform Numer. Algorithms 16 171 185
    • (1997) Numerical Algorithms , vol.16 , Issue.2 , pp. 171-185
    • Lucet, Y.1
  • 27
    • 33847279332 scopus 로고    scopus 로고
    • Fast Moreau envelope computation I: Numerical algorithms
    • Y. Lucet 2006 Fast Moreau envelope computation I: Numerical algorithms Numer. Algorithms 43 235 249
    • (2006) Numer. Algorithms , vol.43 , pp. 235-249
    • Lucet, Y.1
  • 28
    • 1942434208 scopus 로고
    • Propriétés des applications "prox"
    • J.-J. Moreau 1963 Propriétés des applications "prox" C. R. Acad. Sci. Paris 256 1069 1071
    • (1963) C. R. Acad. Sci. Paris , vol.256 , pp. 1069-1071
    • Moreau, J.-J.1
  • 29
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace Hilbertien
    • J.-J. Moreau 1965 Proximité et dualité dans un espace Hilbertien Bull. Soc. Math. France 93 273 299
    • (1965) Bull. Soc. Math. France , vol.93 , pp. 273-299
    • Moreau, J.-J.1
  • 32
    • 0028513617 scopus 로고
    • A fast Legendre transform algorithm and applications to the adhesion model
    • A. Noullez M. Vergassola 1994 A fast Legendre transform algorithm and applications to the adhesion model J. Sci. Comput. 9 259 281
    • (1994) J. Sci. Comput. , vol.9 , pp. 259-281
    • Noullez, A.1    Vergassola, M.2
  • 33
    • 0004267646 scopus 로고
    • Princeton University Press Princeton
    • Rockafellar, R.T.: Convex Analysis. Princeton University Press, Princeton (1970)
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 34
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • R.T. Rockafellar 1976 Monotone operators and the proximal point algorithm SIAM J. Control Optim. 14 877 898
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 36
    • 67449106680 scopus 로고
    • Scilab
    • Scilab. http://www.scilab.org (1994)
    • (1994)
  • 37
    • 6644224525 scopus 로고
    • The inviscid Burgers equation with initial data of Brownian type
    • Z.-S. She E. Aurell U. Frisch 1992 The inviscid Burgers equation with initial data of Brownian type Commun. Math. Phys. 148 623 641
    • (1992) Commun. Math. Phys. , vol.148 , pp. 623-641
    • She, Z.-S.1    Aurell, E.2    Frisch, U.3
  • 38
    • 0242406171 scopus 로고    scopus 로고
    • Three-dimensional Euclidean distance transformation and its application to shortest path planning
    • DOI 10.1016/j.patcog.2003.08.003
    • F.Y. Shih Y.-T. Wu 2004 Fast Euclidean distance transformation in two scans using a 3×3 neighborhood Comput. Vis. Image Underst. 93 195 205
    • (2004) Pattern Recognition , vol.37 , Issue.1 , pp. 79-92
    • Shih, F.Y.1    Wu, Y.-T.2
  • 39
    • 0030356419 scopus 로고    scopus 로고
    • On Computing the Nested Sums and Infimal Convolutions of Convex Piecewise-Linear Functions
    • DOI 10.1006/jagm.1996.0045
    • P. Tseng Z.-Q. Luo 1996 On computing the nested sums and infimal convolutions of convex piecewise-linear functions J. Algorithms 21 240 266
    • (1996) Journal of Algorithms , vol.21 , Issue.2 , pp. 240-266
    • Tseng, P.1    Luo, Z.-Q.2


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