메뉴 건너뛰기




Volumn 31, Issue 3, 2002, Pages 643-657

Optimizing properties of an inertial dynamical system with geometric damping. Link with proximal methods

Author keywords

Dynamical systems in optimization; Entropic methods in optimization; Proximal regularization method; Steepest descent method

Indexed keywords

FUNCTIONS; GEOMETRY; ITERATIVE METHODS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 0036925157     PISSN: 03248569     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Conference Paper
Times cited : (15)

References (24)
  • 1
    • 0035620123 scopus 로고    scopus 로고
    • An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping
    • ALVAREZ, F., and ATTOUCH, H. (2001) An inertial proximal method for maximal monotone operators via discretization of a nonlinear oscillator with damping. Set-Valued Analysis, 9, Issue 1/2, 3-11.
    • (2001) Set-Valued Analysis , vol.9 , Issue.1-2 , pp. 3-11
    • Alvarez, F.1    Attouch, H.2
  • 3
    • 0010753166 scopus 로고
    • Minimization of convex functions on convex sets by means of differential equations
    • (in Russian) Sep. 1994; (English translation: Differential Equations, 30, no. 9, 1365-1375, 1994).
    • ANTIPIN, A.S. (1994) Minimization of convex functions on convex sets by means of differential equations (in Russian). Differentsialnye Uravneniya, 30, no. 9, 1475-1486, Sep. 1994; (English translation: Differential Equations, 30, no. 9, 1365-1375, 1994).
    • (1994) Differentsialnye Uravneniya , vol.30 , Issue.9 , pp. 1475-1486
    • Antipin, A.S.1
  • 4
    • 23044521290 scopus 로고    scopus 로고
    • The heavy ball with friction method, I. The continuous dynamical system: Global exploration of the global minima of a real-valued function by asymptotic analysis of a dissipative dynamical system
    • ATTOUCH, H., GOUDOU, X. and REDONT, P. (2000) The heavy ball with friction method, I. The continuous dynamical system: global exploration of the global minima of a real-valued function by asymptotic analysis of a dissipative dynamical system. Communications in Contemporary Mathematics, 2, 1-34.
    • (2000) Communications in Contemporary Mathematics , vol.2 , pp. 1-34
    • Attouch, H.1    Goudou, X.2    Redont, P.3
  • 6
    • 0033358882 scopus 로고    scopus 로고
    • Interior proximal and multiplier methods based on second order homogeneous kernels
    • AUSLENDER, A., TEBOULLE, M. and BEN-TIBA, S. (1999) Interior proximal and multiplier methods based on second order homogeneous kernels. Mathematics of Operation Research, 24, 645-668.
    • (1999) Mathematics of Operation Research , vol.24 , pp. 645-668
    • Auslender, A.1    Teboulle, M.2    Ben-Tiba, S.3
  • 7
    • 0035924660 scopus 로고    scopus 로고
    • A convergence result for subgradient evolution equations and its application to the steepest descent exponential penalty trajectory in linear programming
    • BAILLON, J.-B. and COMINETTI, R. (2001) A Convergence Result for Subgradient Evolution Equations and its Application to the Steepest Descent Exponential Penalty Trajectory in Linear Programming. Journal of Functional Analysis, 187, 263-273.
    • (2001) Journal of Functional Analysis , vol.187 , pp. 263-273
    • Baillon, J.-B.1    Cominetti, R.2
  • 8
    • 0019397919 scopus 로고
    • Necessary conditions for distributed control problems governed by parabolic variational inequalities
    • BARBU, V. (1981) Necessary conditions for distributed control problems governed by parabolic variational inequalities. SIAM J. on Control and Optimization, 19, 64-86.
    • (1981) SIAM J. on Control and Optimization , vol.19 , pp. 64-86
    • Barbu, V.1
  • 9
    • 85013536596 scopus 로고
    • Opérateurs maximaux monotones
    • North-Holland-American Elsevier
    • BRÉZIS, H. (1973) Opérateurs maximaux monotones. Mathematics Studies 5, North-Holland-American Elsevier.
    • (1973) Mathematics Studies , vol.5
    • Brézis, H.1
  • 10
    • 0002434869 scopus 로고
    • Asymptotic convergence of nonlinear contraction semigroups in Hubert space
    • BRUCK, R.E. (1975) Asymptotic convergence of nonlinear contraction semigroups in Hubert space. Journal of Functional Analysis, 18, 15-26.
    • (1975) Journal of Functional Analysis , vol.18 , pp. 15-26
    • Bruck, R.E.1
  • 11
    • 0031321503 scopus 로고    scopus 로고
    • Coupling the proximal point algorithm with approximation methods
    • COMINETTI, R. (1997) Coupling the proximal point algorithm with approximation methods. J. Optim. Theory Appl., 95, 581-600.
    • (1997) J. Optim. Theory Appl. , vol.95 , pp. 581-600
    • Cominetti, R.1
  • 14
    • 0011423129 scopus 로고    scopus 로고
    • Network games; adaptations to Nash-Cournot equilibrium
    • FLAM, S.D. and HORVATH, CH. (1996) Network games; adaptations to Nash-Cournot equilibrium. Annals of Operations Research, 64, 179-195.
    • (1996) Annals of Operations Research , vol.64 , pp. 179-195
    • Flam, S.D.1    Horvath, Ch.2
  • 15
    • 38249041615 scopus 로고
    • Asymptotic behavior of solutions to a class of nonlinear evolution equations
    • FURUYA, H., MIYASHIBA, K. and KENMOCHI, N. (1986) Asymptotic Behavior of Solutions to a Class of Nonlinear Evolution Equations. Journal of Differential Equations, 62, 73-94.
    • (1986) Journal of Differential Equations , vol.62 , pp. 73-94
    • Furuya, H.1    Miyashiba, K.2    Kenmochi, N.3
  • 17
    • 0031190440 scopus 로고    scopus 로고
    • Proximal mimization methods with generalized Bregman functions
    • KIWIEL, K.C. (1997) Proximal mimization methods with generalized Bregman functions. SIAM J. of Control and Optimization, 35, 4, 1142-1168.
    • (1997) SIAM J. of Control and Optimization , vol.35 , Issue.4 , pp. 1142-1168
    • Kiwiel, K.C.1
  • 18
    • 0347211612 scopus 로고    scopus 로고
    • An asymptotical variational principle associated with the steepest descent method for a convex function
    • LEMAIRE, B. (1996) An asymptotical variational principle associated with the steepest descent method for a convex function. Journal of Convex Analysis, 3, 1, 63-70.
    • (1996) Journal of Convex Analysis , vol.3 , Issue.1 , pp. 63-70
    • Lemaire, B.1
  • 19
    • 0004232443 scopus 로고
    • Contrôle des systèmes distribués singuliers
    • Gauthier-Villars, Paris
    • LIONS, J.-L. (1983) Contrôle des systèmes distribués singuliers. Méthodes Mathématiques de l'Informatique, 13, Gauthier-Villars, Paris.
    • (1983) Méthodes Mathématiques de l'Informatique , vol.13
    • Lions, J.-L.1
  • 20
    • 0012315812 scopus 로고    scopus 로고
    • On the convexity of the multiplicative potential and penalty functions and related topics
    • MARÉCHAL, P. (2001) On the convexity of the multiplicative potential and penalty functions and related topics. Mathematical Programming, Ser. A 89, 505-516.
    • (2001) Mathematical Programming, Ser. A , vol.89 , pp. 505-516
    • Maréchal, P.1
  • 22
    • 0000276924 scopus 로고
    • Proximité et dualité dans un espace hilbertien
    • MOREAU, J.-J. (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
  • 23
    • 0003306861 scopus 로고
    • Introduction to optimization
    • New York
    • POLYAK, B.T. (1987) Introduction to Optimization. Optimization Software, New York.
    • (1987) Optimization Software
    • Polyak, B.T.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.