메뉴 건너뛰기




Volumn 23, Issue 7-8, 2002, Pages 875-890

A splitting method for composite mappings

Author keywords

[No Author keywords available]

Indexed keywords

CONFORMAL MAPPING; INVERSE PROBLEMS; LINEARIZATION; PROBLEM SOLVING; SET THEORY; VARIATIONAL TECHNIQUES;

EID: 0036869086     PISSN: 01630563     EISSN: None     Source Type: Journal    
DOI: 10.1081/NFA-120016274     Document Type: Article
Times cited : (13)

References (33)
  • 1
    • 0001296447 scopus 로고
    • Quantitative stability analysis for maximal monotone operators and semi-groups of contractions
    • Attouch, H.; Moudafi, A.; Riahi, R. Quantitative Stability Analysis for Maximal Monotone Operators and Semi-Groups of Contractions. Nonlinear Anal. 1993, 21(9), 697-723.
    • (1993) Nonlinear Anal. , vol.21 , Issue.9 , pp. 697-723
    • Attouch, H.1    Moudafi, A.2    Riahi, R.3
  • 2
    • 84966251647 scopus 로고
    • Qualitative stability of variational systems, I. The epigraphical distance
    • Attouch, H.; Wets, R.J.-B. Qualitative Stability of Variational Systems, I. The Epigraphical Distance. Trans. Amer. Math. Soc. 1991, 328, 692-729.
    • (1991) Trans. Amer. Math. Soc. , vol.328 , pp. 692-729
    • Attouch, H.1    Wets, R.J.-B.2
  • 4
    • 0004291558 scopus 로고
    • Opérateurs Maximaux Monotones et Semi-Groupes de Contractions Dans Les Espaces de Hilbert
    • North-Holland, Amsterdam
    • Brézis, H. Opérateurs Maximaux Monotones et Semi-Groupes de Contractions Dans Les Espaces de Hilbert. North-Holland, Amsterdam 1973.
    • (1973)
    • Brézis, H.1
  • 5
    • 0002833247 scopus 로고
    • Existence theorems for nonlinear partial differential equations. In global analysis
    • (Proc. Sympos. Pure Math. Vol. XVI, Berkeley, Calif. 1968)
    • Browder, F.E. Existence Theorems for Nonlinear Partial Differential Equations. in Global Analysis (Proc. Sympos. Pure Math. Vol. XVI, Berkeley, Calif. 1968) Amer. Math. Soc. Providence R.I. 1970, 1-60.
    • (1970) Amer. Math. Soc. Providence R.I. , pp. 1-60
    • Browder, F.E.1
  • 6
    • 0031496462 scopus 로고    scopus 로고
    • Convergence rates in forward-backward splitting
    • Chen, G.H.-G.; Rockafellar, R.T. Convergence Rates in Forward-Backward Splitting. SIAM J. Optim. 1997, 7, 421-444.
    • (1997) SIAM J. Optim. , vol.7 , pp. 421-444
    • Chen, G.H.-G.1    Rockafellar, R.T.2
  • 8
    • 0004177997 scopus 로고
    • Splitting methods for monotone operators with applications to parallel optimization
    • Thesis, Massachusetts Institute of Technology
    • Eckstein, J. Splitting Methods for Monotone Operators with Applications to Parallel Optimization. Thesis, Massachusetts Institute of Technology, 1989.
    • (1989)
    • Eckstein, J.1
  • 9
    • 0027113845 scopus 로고
    • On the Douglas-Rachford splitting method and the proximal point algorithm for maximal monotone operators
    • Eckstein, J.; Bertsekas, D. On the Douglas-Rachford Splitting Method and the Proximal Point Algorithm for Maximal Monotone Operators. Math. Programming Ser. A 1992, 55(3), 293-318.
    • (1992) Math. Programming Ser. A , vol.55 , Issue.3 , pp. 293-318
    • Eckstein, J.1    Bertsekas, D.2
  • 10
    • 0012231712 scopus 로고    scopus 로고
    • Operator-splitting methods for monotone affine variational inequalities, with a parallel application to optimal control
    • Eckstein, J.; Ferris, M.C. Operator-splitting Methods for Monotone Affine Variational Inequalities, with a Parallel Application to Optimal Control. Informs J. Comput. 1998, 10(2), 218-235.
    • (1998) Informs J. Comput. , vol.10 , Issue.2 , pp. 218-235
    • Eckstein, J.1    Ferris, M.C.2
  • 11
    • 77957064934 scopus 로고
    • Applications of the method of multipliers to variational inequalities
    • Fortin, M., Glowinski, R., Eds.; North-Holland: Amsterdam
    • Gabay, D. Applications of the Method of Multipliers to Variational Inequalities. In Augmented Lagrangian Methods: Applications to the Solution of Boundary-Value Problems; Fortin, M., Glowinski, R., Eds.; North-Holland: Amsterdam, 1983; 299-331.
    • (1983) Augmented Lagrangian Methods: Applications to the Solution of Boundary-Value Problems , pp. 299-331
    • Gabay, D.1
  • 14
    • 0003778342 scopus 로고    scopus 로고
    • Dualization of monotone generalized equations
    • Ph.D. Thesis, Dept. of Math. University of Washington
    • Pennanen, T. Dualization of Monotone Generalized Equations. Ph.D. Thesis, Dept. of Math. University of Washington, 1999.
    • (1999)
    • Pennanen, T.1
  • 15
    • 0034403146 scopus 로고    scopus 로고
    • Dualization of generalized equations of maximal monotone type
    • Pennanen, T. Dualization of Generalized Equations of Maximal Monotone Type. SIAM J. Optimization 2000, 10, 809-835.
    • (2000) SIAM J. Optimization , vol.10 , pp. 809-835
    • Pennanen, T.1
  • 16
    • 0012339960 scopus 로고    scopus 로고
    • On the range of monotone composite mappings
    • Pennanen, T. On the Range of Monotone Composite Mappings. J. Nonlinear Convex Analysis 2001, 133-202.
    • (2001) J. Nonlinear Convex Analysis , pp. 133-202
    • Pennanen, T.1
  • 17
    • 0012232892 scopus 로고    scopus 로고
    • Variational composition of a monotone operator and a linear mapping with applications to elliptic PDE's with singular coefficients
    • Submitted
    • Pennanen, T.; Rewalski, J.; Théra, M. Variational Composition of a Monotone Operator and a Linear Mapping with Applications to Elliptic PDE's with Singular Coefficients. Submitted.
    • Pennanen, T.1    Rewalski, J.2    Théra, M.3
  • 18
    • 0000056025 scopus 로고
    • Generalized equations and their solutions. I. Basic Theory
    • Robinson, S.M. Generalized Equations and Their Solutions. I. Basic Theory, Math. Programming Stud. 1979, 10, 128-141.
    • (1979) Math. Programming Stud. , vol.10 , pp. 128-141
    • Robinson, S.M.1
  • 19
    • 0002121642 scopus 로고    scopus 로고
    • Composition duality and maximal monotonicity
    • Robinson, S.M. Composition Duality and Maximal Monotonicity. Math. Progr. 1999, 85, 1-13.
    • (1999) Math. Progr. , vol.85 , pp. 1-13
    • Robinson, S.M.1
  • 20
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, NJ
    • Rockafellar, R.T. Convex Analysis; Princeton University Press, Princeton, NJ 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 21
    • 0003450909 scopus 로고
    • Conjugate duality and optimization
    • SIAM Philadelphia, PA
    • Rockafellar, R.T. Conjugate Duality and Optimization. SIAM Philadelphia, PA 1974.
    • (1974)
    • Rockafellar, R.T.1
  • 22
    • 0016985417 scopus 로고
    • Monotone operators and the proximal point algorithm
    • Rockafellar, R.T. Monotone Operators and the Proximal Point Algorithm. SIAM J. Control Optim. 1976, 14, 877-898.
    • (1976) SIAM J. Control Optim. , vol.14 , pp. 877-898
    • Rockafellar, R.T.1
  • 23
    • 0041728515 scopus 로고    scopus 로고
    • Duality and optimality in multistage stochastic programming
    • Rockafellar, R.T. Duality and Optimality in Multistage Stochastic Programming. Ann. Oper. Res. 1999, 85, 1-19.
    • (1999) Ann. Oper. Res. , vol.85 , pp. 1-19
    • Rockafellar, R.T.1
  • 26
    • 0003742136 scopus 로고    scopus 로고
    • A splitting algorithm for multistage stochastic programming with application to hydropower scheduling
    • Ph.D. Thesis, Dept. of Applied Math. University of Washington
    • Salinger, D. A Splitting Algorithm for Multistage Stochastic Programming with Application to Hydropower Scheduling. Ph.D. Thesis, Dept. of Applied Math. University of Washington, 1997.
    • (1997)
    • Salinger, D.1
  • 27
    • 0003608147 scopus 로고    scopus 로고
    • Dynamic splitting: An algorithm for deterministic and stochastic multiperiod optimization
    • Submitted
    • Salinger, D.H.; Rockafellar, R.T. Dynamic Splitting: An Algorithm for Deterministic and Stochastic Multiperiod Optimization, Submitted.
    • Salinger, D.H.1    Rockafellar, R.T.2
  • 28
    • 0012270985 scopus 로고
    • Measurement error model estimation using iteratively weighted least squares
    • Contemp. Math., Brown, P., Fuller, W., Eds.; 112, Amer. Math. Soc.; Providence, RI
    • Schafer, D. Measurement Error Model Estimation Using Iteratively Weighted Least Squares. In Statistical Analysis of Measurement Error Models and Applications; Contemp. Math., Brown, P., Fuller, W., Eds.; 112, Amer. Math. Soc.; Providence, RI, 1990; 129-138.
    • (1990) Statistical Analysis of Measurement Error Models and Applications , pp. 129-138
    • Schafer, D.1
  • 29
    • 0001531775 scopus 로고
    • Partial inverse of a monotone operator
    • Spingarn, J.E. Partial Inverse of a Monotone Operator. Appl. Math. Optim. 1983, 10, 247-265.
    • (1983) Appl. Math. Optim. , vol.10 , pp. 247-265
    • Spingarn, J.E.1
  • 30
    • 0012231728 scopus 로고
    • Sur le Zéros des Opérateurs Maximaux Monotones et Applications
    • Thése d'Etat, Université de Liége
    • Tossings, P. Sur le Zéros des Opérateurs Maximaux Monotones et Applications. Thése d'Etat, Université de Liége, 1990.
    • (1990)
    • Tossings, P.1
  • 31
    • 0026077016 scopus 로고
    • Applications of a splitting algorithm to decomposition in convex programming and variational inequalities
    • Tseng, P. Applications of a Splitting Algorithm to Decomposition in Convex Programming and Variational Inequalities. SIAM J. Control Optim. 1991, 29, 119-138.
    • (1991) SIAM J. Control Optim. , vol.29 , pp. 119-138
    • Tseng, P.1
  • 32
    • 0033884548 scopus 로고    scopus 로고
    • A modified forward-backward splitting method for maximal monotone mappings
    • Tseng, P. A Modified Forward-Backward Splitting Method for Maximal Monotone Mappings. SIAM J. Control Optim. 2000, 38, 431-446.
    • (2000) SIAM J. Control Optim. , vol.38 , pp. 431-446
    • Tseng, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.