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Volumn 15, Issue 1, 2008, Pages 179-190

Self-dual smoothing of convex and saddle functions

Author keywords

Approximation; Convex functions; Duality; Moreau envelopes; Saddle functions

Indexed keywords


EID: 39749115612     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (18)

References (25)
  • 2
    • 39749179434 scopus 로고
    • On continuity properties of the partial Legendre-Fenchel transform: Convergence of sequences of augmented Lagrangian functions, Moreau-Yosida approximates and subdifferential operators
    • J.-B. Hiriart-Urruty ed, North-Holland, Amsterdam
    • H. Attouch, D. Aze, R. J.-B. Wets: On continuity properties of the partial Legendre-Fenchel transform: convergence of sequences of augmented Lagrangian functions, Moreau-Yosida approximates and subdifferential operators, in: Fermat Days 85: Mathematics for Optimization, J.-B. Hiriart-Urruty (ed.), North-Holland, Amsterdam (1986) 1-42.
    • (1986) Fermat Days 85: Mathematics for Optimization , pp. 1-42
    • Attouch, H.1    Aze, D.2    Wets, R.J.-B.3
  • 3
    • 85016656725 scopus 로고
    • Convergence of convex-concave saddle functions: Continuity properties of the Legendre-Fenchel transform and applications to convex programming and mechanics
    • H. Attouch, D. Azé R. J.-B. Wets: Convergence of convex-concave saddle functions: continuity properties of the Legendre-Fenchel transform and applications to convex programming and mechanics, Ann. Inst. H. Poincaré Anal. Non Linéaire 5 (1988) 537-572.
    • (1988) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.5 , pp. 537-572
    • Attouch, H.1    Azé, D.2    Wets, R.J.-B.3
  • 4
    • 84968468130 scopus 로고
    • A convergence theory for saddle functions
    • H. Attouch, R. J.-B. Wets: A convergence theory for saddle functions, Trans. Amer. Math. Soc. 280(1) (1983) 1-41.
    • (1983) Trans. Amer. Math. Soc , vol.280 , Issue.1 , pp. 1-41
    • Attouch, H.1    Wets, R.J.-B.2
  • 6
    • 0343372862 scopus 로고
    • A smoothing technique for nondifferentiable optimization problems
    • Notes Math. 1405, Springer, Berlin
    • A. Ben-Tal, M. Teboulle: A smoothing technique for nondifferentiable optimization problems, in: Optimization (Varetz, 1988), Lect. Notes Math. 1405, Springer, Berlin (1989) 1-11.
    • (1989) Optimization (Varetz, 1988), Lect , pp. 1-11
    • Ben-Tal, A.1    Teboulle, M.2
  • 7
    • 0030303853 scopus 로고    scopus 로고
    • A conjugate duality scheme generating a new class of differentiable duals
    • A. Ben-Tal, M. Teboulle: A conjugate duality scheme generating a new class of differentiable duals, SIAM J. Optim. 6(3) (1996) 617-625.
    • (1996) SIAM J. Optim , vol.6 , Issue.3 , pp. 617-625
    • Ben-Tal, A.1    Teboulle, M.2
  • 8
    • 0036679713 scopus 로고    scopus 로고
    • The problem of optimal smoothing for convex functions
    • M. Ghomi: The problem of optimal smoothing for convex functions, Proc. Amer. Math. Soc. 130(8) (2002) 2255-2259.
    • (2002) Proc. Amer. Math. Soc , vol.130 , Issue.8 , pp. 2255-2259
    • Ghomi, M.1
  • 10
    • 3943095325 scopus 로고    scopus 로고
    • Regularity of the optimal feedback and the value function in convex problems of optimal control
    • R. Goebel: Regularity of the optimal feedback and the value function in convex problems of optimal control, Set-Valued Anal. 12(1-2) (2004) 127-145.
    • (2004) Set-Valued Anal , vol.12 , Issue.1-2 , pp. 127-145
    • Goebel, R.1
  • 11
    • 27644495367 scopus 로고    scopus 로고
    • Convex optimal control problems with smooth Hamiltonians
    • R. Goebel: Convex optimal control problems with smooth Hamiltonians, SIAM J. Control Optim. 43(5) (2005) 1781-1811.
    • (2005) SIAM J. Control Optim , vol.43 , Issue.5 , pp. 1781-1811
    • Goebel, R.1
  • 12
    • 25444461966 scopus 로고    scopus 로고
    • A higher-order smoothing technique for polyhedral convex functions: Geometric and probabilistic considerations
    • S. Guillaume, A. Seeger: A higher-order smoothing technique for polyhedral convex functions: geometric and probabilistic considerations, J. Convex Analysis 8(1) (2001) 109-126.
    • (2001) J. Convex Analysis , vol.8 , Issue.1 , pp. 109-126
    • Guillaume, S.1    Seeger, A.2
  • 13
    • 0040165092 scopus 로고    scopus 로고
    • Practical aspects of the Moreau-Yosida regularization: Theoretical preliminaries
    • C. Lemaréchal, C. Sagastizábal: Practical aspects of the Moreau-Yosida regularization: theoretical preliminaries, SIAM J. Optim. 7(2) (1997) 267-385.
    • (1997) SIAM J. Optim , vol.7 , Issue.2 , pp. 267-385
    • Lemaréchal, C.1    Sagastizábal, C.2
  • 14
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace hilbertien
    • J.-J. Moreau: Proximité et dualité dans un espace hilbertien, Bull. Soc. Math. Fr. 93 (1965) 273-299.
    • (1965) Bull. Soc. Math. Fr , vol.93 , pp. 273-299
    • Moreau, J.-J.1
  • 15
    • 84972561023 scopus 로고
    • A general correspondence between dual minimax problems and convex programs
    • R. T. Rockafellar: A general correspondence between dual minimax problems and convex programs, Pacific J. Math. 25 (1968) 597-611.
    • (1968) Pacific J. Math , vol.25 , pp. 597-611
    • Rockafellar, R.T.1
  • 16
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton
    • R. T. Rockafellar: Convex Analysis, Princeton University Press, Princeton (1970).
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 17
    • 84972555015 scopus 로고
    • Generalized Hamiltonian equations for convex problems of Lagrange
    • R. T. Rockafellar: Generalized Hamiltonian equations for convex problems of Lagrange, Pacific J. Math. 33(2) (1970) 411-427.
    • (1970) Pacific J. Math , vol.33 , Issue.2 , pp. 411-427
    • Rockafellar, R.T.1
  • 18
    • 0043072168 scopus 로고
    • Saddle points of Hamiltonian systems in convex problems of Lagrange
    • R. T. Rockafellar: Saddle points of Hamiltonian systems in convex problems of Lagrange, J. Optimization Theory Appl. 12(4) (1973) 367-390.
    • (1973) J. Optimization Theory Appl , vol.12 , Issue.4 , pp. 367-390
    • Rockafellar, R.T.1
  • 21
    • 0034780555 scopus 로고    scopus 로고
    • Convexity in Hamilton-Jacobi theory. 1: Dynamics and duality
    • R. T. Rockafellar, P. R. Wolenski: Convexity in Hamilton-Jacobi theory. 1: Dynamics and duality, SIAM J. Control Optim. 39(5) (2000) 1323-1350.
    • (2000) SIAM J. Control Optim , vol.39 , Issue.5 , pp. 1323-1350
    • Rockafellar, R.T.1    Wolenski, P.R.2
  • 22
    • 33646762653 scopus 로고    scopus 로고
    • Smoothing a nondifferentiable convex function: The technique of the rolling ball
    • A. Seeger: Smoothing a nondifferentiable convex function: the technique of the rolling ball, Rev. Mat. Apl. 18(1) (1997) 45-60.
    • (1997) Rev. Mat. Apl , vol.18 , Issue.1 , pp. 45-60
    • Seeger, A.1
  • 23
    • 0002417878 scopus 로고    scopus 로고
    • Smoothing a polyhedral convex function via cumulant transformation and homogenization
    • A. Seeger: Smoothing a polyhedral convex function via cumulant transformation and homogenization, Ann. Polon. Math. 67 (1997) 259-268.
    • (1997) Ann. Polon. Math , vol.67 , pp. 259-268
    • Seeger, A.1
  • 24
    • 39749103293 scopus 로고    scopus 로고
    • Personal communication
    • S. Simons: Personal communication (2004).
    • (2004)
    • Simons, S.1
  • 25
    • 0001286634 scopus 로고
    • Entropic proximal mappings with applications to nonlinear programming
    • M. Teboulle: Entropic proximal mappings with applications to nonlinear programming, Math. Oper. Res. 17(3) (1992) 670-690.
    • (1992) Math. Oper. Res , vol.17 , Issue.3 , pp. 670-690
    • Teboulle, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.