메뉴 건너뛰기




Volumn 107, Issue 3, 1998, Pages 720-736

The role of the augmented system in interior point methods

Author keywords

Augmented system; Interior point methods; Linear programming

Indexed keywords

COMPUTATIONAL METHODS; CONSTRAINT THEORY; HEURISTIC METHODS; MATRIX ALGEBRA; PROBLEM SOLVING;

EID: 0032098605     PISSN: 03772217     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0377-2217(97)00074-X     Document Type: Article
Times cited : (21)

References (27)
  • 1
    • 0001351705 scopus 로고
    • On the augmented system approach to sparse least-squares problems
    • M. Arioli, I.S. Duff, P.P.M. Rijk, On the augmented system approach to sparse least-squares problems, Numerische Mathematik 55 (1989) 667-684.
    • (1989) Numerische Mathematik , vol.55 , pp. 667-684
    • Arioli, M.1    Duff, I.S.2    Rijk, P.P.M.3
  • 2
    • 38249011080 scopus 로고
    • Prior reduced fillin solving equations in interior point algorithms
    • J.R. Birge, R.M. Freund, R.J. Vanderbei, Prior reduced fillin solving equations in interior point algorithms, Operations Research Letters 11 (1992) 195-198.
    • (1992) Operations Research Letters , vol.11 , pp. 195-198
    • Birge, J.R.1    Freund, R.M.2    Vanderbei, R.J.3
  • 3
    • 0002877326 scopus 로고
    • Progress in linear programming
    • R.E. Bixby, Progress in Linear Programming, ORSA Journal en Computing 6 (1) (1994) 15-22.
    • (1994) ORSA Journal en Computing , vol.6 , Issue.1 , pp. 15-22
    • Bixby, R.E.1
  • 5
    • 0002189178 scopus 로고
    • Solving symmetric indefinite systems in an interior point method for linear programming
    • R. Fourer, S. Mehrotra, Solving symmetric indefinite systems in an interior point method for linear programming, Mathematical Programming 62 (1993) 15-39.
    • (1993) Mathematical Programming , vol.62 , pp. 15-39
    • Fourer, R.1    Mehrotra, S.2
  • 6
    • 0002850880 scopus 로고
    • Electronic mail distribution of linear programming test problems
    • D.M. Gay, Electronic mail distribution of linear programming test problems, Mathematical Programming Society COAL Newsletter 13 (1985) 10-12.
    • (1985) Mathematical Programming Society COAL Newsletter , vol.13 , pp. 10-12
    • Gay, D.M.1
  • 7
    • 84910914606 scopus 로고
    • Splitting dense columns of constraint matrix in interior point methods for large scale linear programming
    • J Gondzio, Splitting dense columns of constraint matrix in interior point methods for large scale linear programming, Optimization 24 (1992) 285-297.
    • (1992) Optimization , vol.24 , pp. 285-297
    • Gondzio, J.1
  • 8
    • 0026876871 scopus 로고
    • Path following methods for linear programming
    • C.G. Gonzaga, Path following methods for linear programming, SIAM Review 34 (2) (1992) 167-227.
    • (1992) SIAM Review , vol.34 , Issue.2 , pp. 167-227
    • Gonzaga, C.G.1
  • 9
    • 84872985090 scopus 로고
    • Solving large scale linear programming problems using an interior point method on a massively parallel SIMD computer
    • H. Hafsteinsson, R. Levkovitz, G. Mitra, Solving large scale linear programming problems using an interior point method on a massively parallel SIMD computer, Journal of Parallel Algorithms and Applications 4 (3&4) (1994) 301-316.
    • (1994) Journal of Parallel Algorithms and Applications , vol.4 , Issue.3-4 , pp. 301-316
    • Hafsteinsson, H.1    Levkovitz, R.2    Mitra, G.3
  • 10
    • 0027059304 scopus 로고
    • Exploiting special structure in primal dual interior point methods
    • J.K. Hurd, F.H. Murphy, Exploiting special structure in primal dual interior point methods, ORSA Journal on Computing 4 (1) (1992) 38-44.
    • (1992) ORSA Journal on Computing , vol.4 , Issue.1 , pp. 38-44
    • Hurd, J.K.1    Murphy, F.H.2
  • 11
    • 0000114112 scopus 로고
    • Computational experience with a primal-dual interior point method for linear programming
    • I.J. Lustig, R.E. Marsten, D.F. Shanno, Computational experience with a primal-dual interior point method for Linear Programming, Linear Algebra and its Applications 152 (1991) 191-222.
    • (1991) Linear Algebra and Its Applications , vol.152 , pp. 191-222
    • Lustig, I.J.1    Marsten, R.E.2    Shanno, D.F.3
  • 12
    • 0000022796 scopus 로고
    • On implementing Mehrotra's predictor-corrector interior point method for linear programming
    • I.J. Lustig, R.E. Marsten, D.F. Shanno, on implementing Mehrotra's predictor-corrector interior point method for Linear Programming, SIAM Journal on Optimization 2 (1992) 435-449.
    • (1992) SIAM Journal on Optimization , vol.2 , pp. 435-449
    • Lustig, I.J.1    Marsten, R.E.2    Shanno, D.F.3
  • 13
    • 0001662422 scopus 로고
    • Interior point methods for linear programming: Computational state of the art
    • I.J. Lustig, R.E. Marsten, D.F. Shanno, Interior point methods for linear programming: computational state of the art, ORSA Journal on Computing 6 (1) (1994) 1-14.
    • (1994) ORSA Journal on Computing , vol.6 , Issue.1 , pp. 1-14
    • Lustig, I.J.1    Marsten, R.E.2    Shanno, D.F.3
  • 14
  • 16
    • 0041393356 scopus 로고
    • Handling free variables in interior methods
    • Department of Industrial Engineering and Management Sciences, Northwestern University, Evaston, March
    • S. Mehrotra, Handling free variables in interior methods, Technical Report 91-06R1, Department of Industrial Engineering and Management Sciences, Northwestern University, Evaston, March 1991.
    • (1991) Technical Report 91-06R1
    • Mehrotra, S.1
  • 18
    • 0002374308 scopus 로고
    • Solution of large linear programs: A review of hardware, software and algorithmic issues
    • T. Ciriani, R. Leachman (Eds.), Wiley, New York
    • G. Mitra, R. Levkovitz, Solution of large linear programs: a review of hardware, software and algorithmic issues, in: T. Ciriani, R. Leachman (Eds.), Optimization in Industrial Environments, Wiley, New York, 1993, pp. 139-171.
    • (1993) Optimization in Industrial Environments , pp. 139-171
    • Mitra, G.1    Levkovitz, R.2
  • 19
    • 0002778201 scopus 로고
    • Major cholesky would feel proud
    • M.A. Saunders, Major Cholesky would feel proud, ORSA Journal on Computing 6 (1) (1994) 23-27.
    • (1994) ORSA Journal on Computing , vol.6 , Issue.1 , pp. 23-27
    • Saunders, M.A.1
  • 20
    • 84966259276 scopus 로고
    • Modifying pivot elements in Gaussian elimination
    • G.W. Stewart, Modifying pivot elements in Gaussian elimination, Mathematics of Computation 28 (1974) 537.
    • (1974) Mathematics of Computation , vol.28 , pp. 537
    • Stewart, G.W.1
  • 21
    • 0024013802 scopus 로고
    • Exploiting special structure in Karmarkar's linear programming algorithm
    • M.J. Todd, Exploiting special structure in Karmarkar's linear programming algorithm, Mathematical Programming 41 (1988) 81-103.
    • (1988) Mathematical Programming , vol.41 , pp. 81-103
    • Todd, M.J.1
  • 22
    • 0001389460 scopus 로고
    • Computing projections for the Karmarkar algorithm
    • K. Turner, Computing projections for the Karmarkar algorithm, Linear Algebra and its Applications 152 (1991) 141-154.
    • (1991) Linear Algebra and Its Applications , vol.152 , pp. 141-154
    • Turner, K.1
  • 23
    • 0042395506 scopus 로고
    • ALPO: Another linear program optimizer
    • R.J. Vanderbei, ALPO: Another Linear Program Optimizer, ORSA Journal on Computing 3 (2) (1993) 134-146.
    • (1993) ORSA Journal on Computing , vol.3 , Issue.2 , pp. 134-146
    • Vanderbei, R.J.1
  • 24
    • 0022956879 scopus 로고
    • A modification of Karmarkar's linear programming algorithm
    • R.J. Vanderbei, M.S. Meketon, B.F. Freedman, A modification of Karmarkar's linear programming algorithm, Algorithmica 1 (1986) 395-407.
    • (1986) Algorithmica , vol.1 , pp. 395-407
    • Vanderbei, R.J.1    Meketon, M.S.2    Freedman, B.F.3
  • 25
    • 0027911607 scopus 로고
    • Symmetric indefinite systems for interior point methods
    • R.J. Vanderbei, T.J. Carpenter, Symmetric indefinite systems for interior point methods, Mathematical Programming 58 (1993) 1-32.
    • (1993) Mathematical Programming , vol.58 , pp. 1-32
    • Vanderbei, R.J.1    Carpenter, T.J.2
  • 26
    • 0001662428 scopus 로고
    • Interior-point methods: Algorithms and formulations
    • R.J. Vanderbei, Interior-point methods: algorithms and formulations, ORSA Journal on Computing 6 (1) (1994) 32-34.
    • (1994) ORSA Journal on Computing , vol.6 , Issue.1 , pp. 32-34
    • Vanderbei, R.J.1
  • 27
    • 0024303447 scopus 로고
    • Affine scaling for linear programs with free variables
    • R.J. Vanderbei, Affine scaling for linear programs with free variables, Mathematical Programming 43 (1989) 31-44.
    • (1989) Mathematical Programming , vol.43 , pp. 31-44
    • Vanderbei, R.J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.