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Volumn 96, Issue 1, 1998, Pages 159-173

Subgradient method with entropic projections for convex nondifferentiable minimization

Author keywords

Convex programming; entropic projections; nondifferentiable optimization; subgradient algorithms

Indexed keywords

CONSTRAINED OPTIMIZATION;

EID: 0032331714     PISSN: 00223239     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1022671302532     Document Type: Article
Times cited : (5)

References (29)
  • 2
    • 0002450802 scopus 로고
    • Minimization of Unsmooth Functional
    • Russian
    • POLYAK, B. T., Minimization of Unsmooth Functional, Zhurnal Vychislitielnoj Matematiki i Matematicheskoj Fiziki, Vol. 9, pp. 509-521, 1969 (Russian); English Translation in USSR Computational Mathematics and Mathematical Physics, Vol. 9, pp. 14-29, 1969.
    • (1969) Zhurnal Vychislitielnoj Matematiki I Matematicheskoj Fiziki , vol.9 , pp. 509-521
    • Polyak, B.T.1
  • 3
    • 0344864610 scopus 로고
    • English Translation
    • POLYAK, B. T., Minimization of Unsmooth Functional, Zhurnal Vychislitielnoj Matematiki i Matematicheskoj Fiziki, Vol. 9, pp. 509-521, 1969 (Russian); English Translation in USSR Computational Mathematics and Mathematical Physics, Vol. 9, pp. 14-29, 1969.
    • (1969) USSR Computational Mathematics and Mathematical Physics , vol.9 , pp. 14-29
  • 4
    • 38249002574 scopus 로고
    • An Improved Subgradient Method for Constrained Nondifferentiable Optimization
    • KIM, S., and UM, B. S., An Improved Subgradient Method for Constrained Nondifferentiable Optimization, Operations Research Letters, Vol. 14, pp. 61-64, 1993.
    • (1993) Operations Research Letters , vol.14 , pp. 61-64
    • Kim, S.1    Um, B.S.2
  • 5
    • 0030104971 scopus 로고    scopus 로고
    • The Efficiency of Subgradient Projection Methods for Convex Optimization, Part 2: Implementations and Extensions
    • KIWIEL, K. C., The Efficiency of Subgradient Projection Methods for Convex Optimization, Part 2: Implementations and Extensions, SIAM Journal on Control and Optimization, Vol. 34, pp. 677-697, 1996.
    • (1996) SIAM Journal on Control and Optimization , vol.34 , pp. 677-697
    • Kiwiel, K.C.1
  • 8
    • 0003613190 scopus 로고
    • Naukova Dumka, Kiev, Russian; English Translation by Springer Verlag, Berlin, Germany
    • SHOR, N. Z., Minimization Methods for Nondifferentiable Functions, Naukova Dumka, Kiev, 1979 (Russian); English Translation by Springer Verlag, Berlin, Germany, 1985.
    • (1979) Minimization Methods for Nondifferentiable Functions
    • Shor, N.Z.1
  • 9
    • 0001286634 scopus 로고
    • Entropic Proximal Mappings with Applications to Nonlinear Programming
    • TEBOULLE, M., Entropic Proximal Mappings with Applications to Nonlinear Programming, Mathematics of Operations Research, Vol. 17, pp. 670-690, 1992.
    • (1992) Mathematics of Operations Research , vol.17 , pp. 670-690
    • Teboulle, M.1
  • 11
    • 0001263852 scopus 로고
    • Finding a Common Point of Convex Sets by the Method of Successive Projections
    • Russian
    • BREGMAN, L. M., Finding a Common Point of Convex Sets by the Method of Successive Projections, Doklady Akademii Nauk SSSR, Vol. 162, pp. 487-490, 1965 (Russian); English Translation in Soviet Mathematical Doklady, Vol. 6, pp. 688-692, 1965.
    • (1965) Doklady Akademii Nauk SSSR , vol.162 , pp. 487-490
    • Bregman, L.M.1
  • 12
    • 0001336448 scopus 로고
    • English Translation
    • BREGMAN, L. M., Finding a Common Point of Convex Sets by the Method of Successive Projections, Doklady Akademii Nauk SSSR, Vol. 162, pp. 487-490, 1965 (Russian); English Translation in Soviet Mathematical Doklady, Vol. 6, pp. 688-692, 1965.
    • (1965) Soviet Mathematical Doklady , vol.6 , pp. 688-692
  • 13
    • 0031146730 scopus 로고    scopus 로고
    • Free-Steering Relaxation Methods for Problems with Strictly Convex Costs and Linear Constraints
    • KIWIEL, K. C., Free-Steering Relaxation Methods for Problems with Strictly Convex Costs and Linear Constraints, Mathematics of Operations Research, Vol. 22, pp. 326-379, 1997.
    • (1997) Mathematics of Operations Research , vol.22 , pp. 326-379
    • Kiwiel, K.C.1
  • 14
    • 0019587748 scopus 로고
    • An Iterative Row-Action Method for Interval Convex Programming
    • CENSOR, Y., and LENT, A., An Iterative Row-Action Method for Interval Convex Programming, Journal of Optimization Theory and Applications, Vol. 34, pp. 321-353, 1981.
    • (1981) Journal of Optimization Theory and Applications , vol.34 , pp. 321-353
    • Censor, Y.1    Lent, A.2
  • 15
    • 0029207145 scopus 로고
    • An Interior-Proximal Method for Convex Linearly Constrained Problems and Its Extension to Variational Inequalities
    • AUSLENDER, A., and HADDOU, M., An Interior-Proximal Method for Convex Linearly Constrained Problems and Its Extension to Variational Inequalities, Mathematical Programming, Vol. 71, pp. 77-100, 1995.
    • (1995) Mathematical Programming , vol.71 , pp. 77-100
    • Auslender, A.1    Haddou, M.2
  • 16
    • 0000433247 scopus 로고
    • Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions
    • CHEN, G., and TEBOULLE, M., Convergence Analysis of a Proximal-Like Minimization Algorithm Using Bregman Functions, SIAM Journal on Optimization, Vol. 3, pp. 538-543, 1993.
    • (1993) SIAM Journal on Optimization , vol.3 , pp. 538-543
    • Chen, G.1    Teboulle, M.2
  • 17
    • 0001702688 scopus 로고
    • Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming
    • ECKSTEIN, B., Nonlinear Proximal Point Algorithms Using Bregman Functions, with Applications to Convex Programming, Mathematics of Operations Research, Vol. 18, pp. 202-226, 1993.
    • (1993) Mathematics of Operations Research , vol.18 , pp. 202-226
    • Eckstein, B.1
  • 19
    • 0000019392 scopus 로고
    • Convergence Rate Analysis of Nonquadratic Proximal and Augmented Lagrangian Methods for Convex and Linear Programming
    • IUSEM, A. N., and TEBOULLE, M., Convergence Rate Analysis of Nonquadratic Proximal and Augmented Lagrangian Methods for Convex and Linear Programming, Mathematics of Operations Research, Vol. 30, pp. 657-677, 1995.
    • (1995) Mathematics of Operations Research , vol.30 , pp. 657-677
    • Iusem, A.N.1    Teboulle, M.2
  • 20
    • 0031190440 scopus 로고    scopus 로고
    • Proximal Minimization Methods with Generalized Bregman Functions
    • KIWIEL, K. C., Proximal Minimization Methods with Generalized Bregman Functions, SIAM Journal on Control and Optimization, Vol. 35, pp. 1142-1168, 1997.
    • (1997) SIAM Journal on Control and Optimization , vol.35 , pp. 1142-1168
    • Kiwiel, K.C.1
  • 21
    • 0041629347 scopus 로고    scopus 로고
    • Nonlinear Rescaling and Proximal-Like Methods in Convex Optimization
    • POLYAK, R., and TEBOULLE, M., Nonlinear Rescaling and Proximal-Like Methods in Convex Optimization, Mathematical Programming, Vol. 76, pp. 265-284, 1997.
    • (1997) Mathematical Programming , vol.76 , pp. 265-284
    • Polyak, R.1    Teboulle, M.2
  • 23
    • 0003359547 scopus 로고
    • Lagrangian Relaxation
    • Edited by C. R. Reeves, Blackwell Scientific Publications, Oxford, England
    • BEASLEY, J. E., Lagrangian Relaxation, Modern Heuristic Techniques for Combinatorial Problems, Edited by C. R. Reeves, Blackwell Scientific Publications, Oxford, England, pp. 243-303, 1993.
    • (1993) Modern Heuristic Techniques for Combinatorial Problems , pp. 243-303
    • Beasley, J.E.1
  • 24
    • 0022031091 scopus 로고
    • An Applications Oriented Guide to Lagrangian Relaxation
    • FISHER, M. L., An Applications Oriented Guide to Lagrangian Relaxation, Interfaces, Vol. 15, pp. 10-21, 1985.
    • (1985) Interfaces , vol.15 , pp. 10-21
    • Fisher, M.L.1
  • 27
    • 84947907790 scopus 로고    scopus 로고
    • A Heuristic Algorithm for the Set Covering Problem
    • Integer Programming and Combinatorial Optimization, Edited by W. H. Cunningham, S. T. McCormick, and M. Queyranne, Springer Verlag, Berlin, Germany
    • CAPRARA, A., FISCHETTI, M., and TOTH, P., A Heuristic Algorithm for the Set Covering Problem, Integer Programming and Combinatorial Optimization, Edited by W. H. Cunningham, S. T. McCormick, and M. Queyranne, Lecture Notes in Computer Science, Springer Verlag, Berlin, Germany, Vol. 1084, pp. 72-84, 1996.
    • (1996) Lecture Notes in Computer Science , vol.1084 , pp. 72-84
    • Caprara, A.1    Fischetti, M.2    Toth, P.3
  • 28
    • 0004267646 scopus 로고
    • Princeton University Press, Princeton, New Jersey
    • ROCKAFELLAR, R. T., Convex Analysis, Princeton University Press, Princeton, New Jersey, 1970.
    • (1970) Convex Analysis
    • Rockafellar, R.T.1
  • 29
    • 0030110299 scopus 로고    scopus 로고
    • The Efficiency of Subgradient Projection Methods for Convex Optimization, Part 1: General Level Methods
    • KIWIEL, K. C., The Efficiency of Subgradient Projection Methods for Convex Optimization, Part 1: General Level Methods, SIAM Journal on Control and Optimization, Vol. 34, pp. 660-676, 1996.
    • (1996) SIAM Journal on Control and Optimization , vol.34 , pp. 660-676
    • Kiwiel, K.C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.