메뉴 건너뛰기




Volumn 37, Issue 4, 1996, Pages 323-339

Iterations of paracontractions and firmly nonexpansive operators with applications to feasibility and optimization

Author keywords

Asymptotic fixed point; Bregman function; Firmly nonexpansive; Generalized distance; Paracontractions; Projection; Repetitive control

Indexed keywords


EID: 0030456727     PISSN: 02331934     EISSN: None     Source Type: Journal    
DOI: 10.1080/02331939608844225     Document Type: Article
Times cited : (256)

References (33)
  • 1
    • 0011353229 scopus 로고
    • An interior points algorithm for the convex feasibility problem
    • Aharoni, R. Berman, A. and Censor, Y. (1983) An interior points algorithm for the convex feasibility problem, Advances in Applied Mathematics, 4, 479-489
    • (1983) Advances in Applied Mathematics , vol.4 , pp. 479-489
    • Aharoni, R.1    Berman, A.2    Censor, Y.3
  • 2
    • 0011311155 scopus 로고
    • On projection algorithms for solving convex feasibility problems
    • Research Report 93-12, Dept. of Mathematics and Statistics, Simon Fraser University, Burnaby, B.C., Canada, June, to appear
    • Bauschke, H. H. and Borwein, J. M. (1993) On projection algorithms for solving convex feasibility problems, Research Report 93-12, Dept. of Mathematics and Statistics, Simon Fraser University, Burnaby, B.C., Canada, June. SIAM Review, to appear
    • (1993) SIAM Review
    • Bauschke, H.H.1    Borwein, J.M.2
  • 4
    • 49949144765 scopus 로고
    • The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming
    • Bregman, L. M. (1967) The relaxation method of finding the common point of convex sets and its application to the solution of problems in convex programming, USSR Computational Mathematics and Mathematical Physics, 7, 200-217
    • (1967) USSR Computational Mathematics and Mathematical Physics , vol.7 , pp. 200-217
    • Bregman, L.M.1
  • 5
    • 5744237139 scopus 로고
    • On the behavior of a block-iterative projection method for solving convex feasibility problems
    • Butnariu, D. and Censor, Y. (1990) On the behavior of a block-iterative projection method for solving convex feasibility problems, International Journal of Computer Mathematics, 34, 79-94
    • (1990) International Journal of Computer Mathematics , vol.34 , pp. 79-94
    • Butnariu, D.1    Censor, Y.2
  • 6
    • 0027190119 scopus 로고
    • Iterative image reconstruction algorithms based on cross-entropy minimization
    • Erratum and Addendum, ibid., 4, 225-226, 1995
    • Byrne, C. L. (1993) Iterative image reconstruction algorithms based on cross-entropy minimization, IEEE Transactions on Image Processing, 2, 96-103. Erratum and Addendum, ibid., 4, 225-226, 1995
    • (1993) IEEE Transactions on Image Processing , vol.2 , pp. 96-103
    • Byrne, C.L.1
  • 7
    • 0000439725 scopus 로고
    • Row-action methods for huge and sparse systems and their applications
    • Censor, Y. (1981) Row-action methods for huge and sparse systems and their applications, SIAM Review, 23, 444-464
    • (1981) SIAM Review , vol.23 , pp. 444-464
    • Censor, Y.1
  • 8
    • 34250085515 scopus 로고
    • Parallel application of block-iterative methods in medical imaging and radiation therapy
    • Censor, Y. (1988) Parallel application of block-iterative methods in medical imaging and radiation therapy, Mathematical Programming, 42, 307-325
    • (1988) Mathematical Programming , vol.42 , pp. 307-325
    • Censor, Y.1
  • 9
  • 10
    • 0001199422 scopus 로고
    • On iterative methods for linearly constrained entropy maximization
    • (Wakulicz, A.Editor), Banach Center Publications XXIX, PWN-Polish Scientific Publishers, Warsaw, Poland
    • Censor, Y. De Pierro, A. R. Elfving, T. Herman, G. T. and Iusem, A. N. (1990) On iterative methods for linearly constrained entropy maximization, in: Numerical Analysis and Mathematical Modelling, (Wakulicz, A.Editor), Banach Center Publications XXIX, PWN-Polish Scientific Publishers, Warsaw, Poland, pp. 145-163
    • (1990) Numerical Analysis and Mathematical Modelling , pp. 145-163
    • Censor, Y.1    De Pierro, A.R.2    Elfving, T.3    Herman, G.T.4    Iusem, A.N.5
  • 13
    • 0000424337 scopus 로고
    • A multiprojection algorithm using Bregman projections in a product space
    • Censor, Y. and Elfving, T. (1994) A multiprojection algorithm using Bregman projections in a product space, Numerical Algorithms, 8, 221-239
    • (1994) Numerical Algorithms , vol.8 , pp. 221-239
    • Censor, Y.1    Elfving, T.2
  • 15
    • 0000433247 scopus 로고
    • Convergence analysis of a proximal-like optimization algorithm using Bregman functions
    • Chen, G. and Teboulle, M. (1993) Convergence analysis of a proximal-like optimization algorithm using Bregman functions, SIAM Journal on Optimization, 3, 538-543
    • (1993) SIAM Journal on Optimization , vol.3 , pp. 538-543
    • Chen, G.1    Teboulle, M.2
  • 16
    • 0027541192 scopus 로고
    • The foundations of set theoretic estimation
    • Combettes, P. L. (1993) The foundations of set theoretic estimation, Proceedings of The IEEE, 81, 182-208
    • (1993) Proceedings of The IEEE , vol.81 , pp. 182-208
    • Combettes, P.L.1
  • 17
    • 0025595687 scopus 로고
    • Why least squares and maximum entropy? An axoimatic approach to inference for linear inverse problems
    • Csiszár, I. (1991) Why least squares and maximum entropy? An axoimatic approach to inference for linear inverse problems, The Annals of Statistics, 19, 2032-2066
    • (1991) The Annals of Statistics , vol.19 , pp. 2032-2066
    • Csiszár, I.1
  • 19
    • 0000876601 scopus 로고
    • Random products of nonexpansive mappings
    • (A. Ioffe, M. Marcus and S. Reich, Editors), Longman Scientific and Technical, Harlow, Great Britain
    • Dye, J. M. and Reich, S. (1992) Random products of nonexpansive mappings, in; "Optimization and Nonlinear Analysis", (A. Ioffe, M. Marcus and S. Reich, Editors), Longman Scientific and Technical, Harlow, Great Britain pp. 106-118
    • (1992) Optimization and Nonlinear Analysis , pp. 106-118
    • Dye, J.M.1    Reich, S.2
  • 20
    • 0001702688 scopus 로고
    • Nonlinear proximal point algorithms using Bregman functions with applications to convex programming
    • Eckstein, J. (1993) Nonlinear proximal point algorithms using Bregman functions with applications to convex programming, Mathematics of Operations Research, 18, 202-226
    • (1993) Mathematics of Operations Research , vol.18 , pp. 202-226
    • Eckstein, J.1
  • 21
    • 0002815417 scopus 로고
    • Multiplicative iterative algorithms for convex programming
    • Eggermont, P. P. B. (1990) Multiplicative iterative algorithms for convex programming, linear Algebra and Its Applications, 130, 25-42
    • (1990) Linear Algebra and Its Applications , vol.130 , pp. 25-42
    • Eggermont, P.P.B.1
  • 22
    • 0024945769 scopus 로고
    • An algorithm for maximum entropy image reconstruction from noisy data
    • Elfving, T. (1989) An algorithm for maximum entropy image reconstruction from noisy data, Mathematical and Computer Modelling, 12, 729-745
    • (1989) Mathematical and Computer Modelling , vol.12 , pp. 729-745
    • Elfving, T.1
  • 23
    • 0000695406 scopus 로고
    • Convergence of sequential asynchronous nonlinear paracontractions
    • Elsner, L. Koltracht, I. and Neumann, M. (1992) Convergence of sequential asynchronous nonlinear paracontractions, Numerische Mathematik, 62, 305-319
    • (1992) Numerische Mathematik , vol.62 , pp. 305-319
    • Elsner, L.1    Koltracht, I.2    Neumann, M.3
  • 27
    • 0011311504 scopus 로고
    • On dual convergence and the rate of primal convergence of Bregman's convex programming method
    • Iusem, A. N. (1991) On dual convergence and the rate of primal convergence of Bregman's convex programming method, SIAM Journal on Optimization, 1, 401-423
    • (1991) SIAM Journal on Optimization , vol.1 , pp. 401-423
    • Iusem, A.N.1
  • 28
    • 0345295872 scopus 로고
    • Block-iterative surrogate projection methods for convex feasibility problems
    • Kiwiel, K. C. (1995) Block-iterative surrogate projection methods for convex feasibility problems, Linear Algebra and its Applications, 215, 225-259
    • (1995) Linear Algebra and Its Applications , vol.215 , pp. 225-259
    • Kiwiel, K.C.1
  • 29
    • 0021201713 scopus 로고
    • Decomposition through formalization in a product space
    • Pierra, G. (1984) Decomposition through formalization in a product space, Mathematical Programming, 28, 96-115
    • (1984) Mathematical Programming , vol.28 , pp. 96-115
    • Pierra, G.1
  • 31
    • 0001286634 scopus 로고
    • Entropie proximal mappings with applications to nonlinear programming
    • Teboulle, M. (1992) Entropie proximal mappings with applications to nonlinear programming, Mathematics of Operations Research, 17, 670-690
    • (1992) Mathematics of Operations Research , vol.17 , pp. 670-690
    • Teboulle, M.1
  • 32
    • 0000320937 scopus 로고
    • On the convergence of the products of firmly nonexpansive mappings
    • Tseng, P. (1992) On the convergence of the products of firmly nonexpansive mappings, SIAM Journal on Optimization, 2, 425-434
    • (1992) SIAM Journal on Optimization , vol.2 , pp. 425-434
    • Tseng, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.