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Volumn 4, Issue 2, 1997, Pages 235-255

Minimization of nonsmooth convex functionals in Banach spaces

Author keywords

Banach spaces; Generalized projection; Metric projection; Nonsmooth optimization; Subgradient methods; Weak convergence

Indexed keywords


EID: 21944448574     PISSN: 09446532     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (39)

References (17)
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    • Metric and generalized projection operators in Danach spaces: Properties and applications
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    • Ya. I. Alber: Metric and generalized projection operators in Danach spaces: Properties and applications, In A. Kartsatos, editor, Theory and Applications of Nonlinear Operators of Accretive and Monotone Types, Marcel Dekker, Inc., New York (1996) 15-50.
    • (1996) Theory and Applications of Nonlinear Operators of Accretive and Monotone Types , pp. 15-50
    • Alber, Ya.I.1
  • 3
    • 0002780670 scopus 로고    scopus 로고
    • Iterative solution of unstable variational inequalities on approximately given sets
    • Ya. I. Alber, A. Kartsatos, and E. Litsyn: Iterative solution of unstable variational inequalities on approximately given sets, Abstract and Applied Analysis, 1(1) (1996) 45-65.
    • (1996) Abstract and Applied Analysis , vol.1 , Issue.1 , pp. 45-65
    • Alber, Ya.I.1    Kartsatos, A.2    Litsyn, E.3
  • 4
    • 0001016179 scopus 로고
    • Geometric properties of Danach spaces and approximate methods for solving nonlinear operator equations
    • Ya. I. Alber, A. I Notik: Geometric properties of Danach spaces and approximate methods for solving nonlinear operator equations, Soviet Math. Dokl., 29 (1984) 611-615.
    • (1984) Soviet Math. Dokl. , vol.29 , pp. 611-615
    • Alber, Ya.I.1    Notik, A.I.2
  • 5
    • 0041506823 scopus 로고
    • On minimization of functional and solution of variational inequalities in Danach spaces
    • Ya. I. Alber, A. I Notik: On minimization of functional and solution of variational inequalities in Danach spaces, Soviet Math. Dokl., 34(2) (1987) 296-300.
    • (1987) Soviet Math. Dokl. , vol.34 , Issue.2 , pp. 296-300
    • Alber, Ya.I.1    Notik, A.I.2
  • 6
    • 0011533473 scopus 로고
    • Parallelogram inequalities in Danach spaces and some properties of the duality mapping
    • Ya. I. Alber, A. I Notik: Parallelogram inequalities in Danach spaces and some properties of the duality mapping, Ukranian Math. Journal, 40 (1988) 650-652.
    • (1988) Ukranian Math. Journal , vol.40 , pp. 650-652
    • Alber, Ya.I.1    Notik, A.I.2
  • 7
    • 25444479204 scopus 로고
    • On the iterative method for variational inequalities with nonsmooth unbounded operators in Danach space
    • Ya. I. Alber, A. I Notik: On the iterative method for variational inequalities with nonsmooth unbounded operators in Danach space, Journal of Mathematical Analysis and Applications, 188(3) (1994) 928-939.
    • (1994) Journal of Mathematical Analysis and Applications , vol.188 , Issue.3 , pp. 928-939
    • Alber, Ya.I.1    Notik, A.I.2
  • 9
    • 33646971357 scopus 로고
    • Convergence of some algorithms for convex minimization
    • R. Correa, C. Lemaréchal: Convergence of some algorithms for convex minimization, Mathematical Programming, 62 (1993) 261-275.
    • (1993) Mathematical Programming , vol.62 , pp. 261-275
    • Correa, R.1    Lemaréchal, C.2
  • 10
    • 25444515255 scopus 로고
    • The geometry of Danach spaces
    • Springer-Verlag, Derlin
    • J. Diestel: The geometry of Danach spaces, Lecture Notes in Mathematics 485, Springer-Verlag, Derlin, 1975.
    • (1975) Lecture Notes in Mathematics 485
    • Diestel, J.1
  • 11
    • 0002811034 scopus 로고
    • On the muduli of convexity and smoothness
    • T. Figiel: On the muduli of convexity and smoothness, Studia Mathematica, 56 (1976) 121-155.
    • (1976) Studia Mathematica , vol.56 , pp. 121-155
    • Figiel, T.1
  • 12
    • 0003486420 scopus 로고
    • Convex analysis with applications to differentiation of convex functions
    • Pitman, Doston
    • J. R. Giles: Convex analysis with applications to differentiation of convex functions, Research notes in mathematics 58, Pitman, Doston, 1982.
    • (1982) Research Notes in Mathematics , vol.58
    • Giles, J.R.1
  • 14
    • 84956215235 scopus 로고
    • Geometrie theory of Banach spaces. Part II: Geometry of the unit sphere
    • V. D. Milman: Geometrie theory of Banach spaces. Part II: Geometry of the unit sphere, Russian Mathematics Surveys, 26(6) (1971) 79-163.
    • (1971) Russian Mathematics Surveys , vol.26 , Issue.6 , pp. 79-163
    • Milman, V.D.1
  • 15
    • 0000686629 scopus 로고
    • A general method of solving extremum problems
    • B. T. Polyak: A general method of solving extremum problems, Soviet Math. Dokl, 8 (1967) 593-597.
    • (1967) Soviet Math. Dokl , vol.8 , pp. 593-597
    • Polyak, B.T.1
  • 16
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    • Optimization Software, Inc., Publications Division, New York
    • B. T. Polyak: Introduction to Optimization, Optimization Software, Inc., Publications Division, New York, 1987.
    • (1987) Introduction to Optimization
    • Polyak, B.T.1
  • 17
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    • Convergence of mean iterates for nonlinear monotone equations in Banach space
    • In Russian
    • I. P. Ryazantseva: Convergence of mean iterates for nonlinear monotone equations in Banach space, Vestnik Moscovskogo Universiteta, Series XV, 4 (1987) 61-63. (In Russian).
    • (1987) Vestnik Moscovskogo Universiteta, Series XV , vol.4 , pp. 61-63
    • Ryazantseva, I.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.