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Volumn 28, Issue 2, 2004, Pages 197-215

A new decomposition technique in solving multistage stochastic linear programs by infeasible interior point methods

Author keywords

Decomposition; Infeasible primal dual interior point method; Scenario analysis; Stochastic linear programs

Indexed keywords

CONSTRAINT THEORY; DECISION MAKING; MATHEMATICAL MODELS; NUMERICAL METHODS; PROBLEM SOLVING; STOCHASTIC PROGRAMMING; UNCERTAIN SYSTEMS;

EID: 1542315959     PISSN: 09255001     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:JOGO.0000015311.63755.01     Document Type: Article
Times cited : (12)

References (30)
  • 1
    • 84990704714 scopus 로고
    • Performance of a benchmark parallel implementation of the van Slyke and wets algorithm for two-stage stochastic programs on the sequent/balance
    • Ariyawansa, K.A. and Hudson, D.D. (1991), Performance of a benchmark parallel implementation of the Van Slyke and Wets algorithm for two-stage stochastic programs on the Sequent/Balance, Concurrency Practice and Experience, 3, 109-128.
    • (1991) Concurrency Practice and Experience , vol.3 , pp. 109-128
    • Ariyawansa, K.A.1    Hudson, D.D.2
  • 2
    • 0029336061 scopus 로고
    • A cutting plane method from analytic centers for stochastic programming
    • Bahn, O., du Merle, O., Goffin, J.-L. and Vial, J.P., (1995), A cutting plane method from analytic centers for stochastic programming, Math. Program., 69, 45-73.
    • (1995) Math. Program. , vol.69 , pp. 45-73
    • Bahn, O.1    Du Merle, O.2    Goffin, J.-L.3    Vial, J.P.4
  • 3
    • 0036759227 scopus 로고    scopus 로고
    • A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming
    • Berkelaar, A., Dert, C., Oldenkamp, B. and Zhang, S. (2002), A primal-dual decomposition-based interior point approach to two-stage stochastic linear programming, Oper. Res., 50, 904-915.
    • (2002) Oper. Res. , vol.50 , pp. 904-915
    • Berkelaar, A.1    Dert, C.2    Oldenkamp, B.3    Zhang, S.4
  • 4
    • 1542352143 scopus 로고    scopus 로고
    • A primal-dual decomposition algorithm for multistage stochastic convex programming
    • Tech. Report SEEM2000-07, The Chinese University of Hong Kong
    • Berkelaar, A., Kouwenberg, R. and Zhang, S. (2000), A primal-dual decomposition algorithm for multistage stochastic convex programming, Tech. Report SEEM2000-07, The Chinese University of Hong Kong.
    • (2000)
    • Berkelaar, A.1    Kouwenberg, R.2    Zhang, S.3
  • 5
    • 0042741398 scopus 로고
    • Current trends in stochastic programming computation and applications
    • Tech. Report 95-15, Department of Industrial and Operations Engineering, University of Michigan
    • Birge, J.R. (1995), Current trends in stochastic programming computation and applications, Tech. Report 95-15, Department of Industrial and Operations Engineering, University of Michigan.
    • (1995)
    • Birge, J.R.1
  • 6
    • 0027002128 scopus 로고
    • Efficient solutions of two-stage stochastic linear programs using interior point methods
    • Birge, J.R. and Holmes, D.F. (1992), Efficient solutions of two-stage stochastic linear programs using interior point methods, Computational Optim. Appl., 1, 245-276.
    • (1992) Computational Optim. Appl. , vol.1 , pp. 245-276
    • Birge, J.R.1    Holmes, D.F.2
  • 8
    • 0001238788 scopus 로고
    • Computing block-angular Karmarkar projections with applications to stochastic programming
    • Birge, J.R. and Qi, L. (1988), Computing block-angular Karmarkar projections with applications to stochastic programming, Management Science, 34, 1472-1479.
    • (1988) Management Science , vol.34 , pp. 1472-1479
    • Birge, J.R.1    Qi, L.2
  • 9
    • 0001380612 scopus 로고
    • Formolating stochastic programs for interior point methods
    • Carpenter, T., Lustig, I. and Mulvey, J. (1991), Formolating stochastic programs for interior point methods, Oper. Res., 39, 757-770.
    • (1991) Oper. Res. , vol.39 , pp. 757-770
    • Carpenter, T.1    Lustig, I.2    Mulvey, J.3
  • 10
    • 84936479732 scopus 로고
    • Scenario analysis modeling and decomposition methods
    • Tech. Report 92-8, Department of Industrial Engineering, University of Wisconsin-Madison
    • Chun, B.J. (1992), Scenario analysis modeling and decomposition methods, Tech. Report 92-8, Department of Industrial Engineering, University of Wisconsin-Madison.
    • (1992)
    • Chun, B.J.1
  • 11
    • 21844501022 scopus 로고
    • Scenario analysis via bandle decomposition
    • Chun, B.J. and Robinson, S.M. (1995), Scenario analysis via bandle decomposition, Ann. Oper. Res., 56, 39-63.
    • (1995) Ann. Oper. Res. , vol.56 , pp. 39-63
    • Chun, B.J.1    Robinson, S.M.2
  • 12
    • 0343691647 scopus 로고
    • Approximate scenario solations in the progressive hedging algorithm
    • Helgason, T. and Wallace, S.W. (1991), Approximate scenario solations in the progressive hedging algorithm, Ann. Oper. Res., 31, 425-444.
    • (1991) Ann. Oper. Res. , vol.31 , pp. 425-444
    • Helgason, T.1    Wallace, S.W.2
  • 13
    • 0003881770 scopus 로고    scopus 로고
    • Stochastic decomposition: A statistical method for large-scale stochastic linear programming
    • Kluwer Academic Publishers, Dordrecht, The Netherlands
    • Higle, J.L. and Sen, S. (1996), Stochastic Decomposition: a statistical method for large-scale stochastic linear programming, Kluwer Academic Publishers, Dordrecht, The Netherlands.
    • (1996)
    • Higle, J.L.1    Sen, S.2
  • 14
    • 0027667652 scopus 로고
    • A primal-dual infeasible-interior-point algorithm for linear programming
    • Kojima, M., Megiddo, N. and Mizuno, S. (1993), A primal-dual infeasible-interior-point algorithm for linear programming, Math. Program., 61, 263-280.
    • (1993) Math. Program. , vol.61 , pp. 263-280
    • Kojima, M.1    Megiddo, N.2    Mizuno, S.3
  • 15
    • 9744257292 scopus 로고
    • Feasibility issues in a primal-dual interior point method for linear programming
    • Lustig, L.J. (1990), Feasibility issues in a primal-dual interior point method for linear programming, Math. Program., 49, 145-162.
    • (1990) Math. Program. , vol.49 , pp. 145-162
    • Lustig, L.J.1
  • 16
    • 0000561116 scopus 로고
    • On the implementation of a primal-dual interior point method
    • Mehrotra, S. (1992), On the implementation of a primal-dual interior point method, SIAM J. Optim., 2, 575-601.
    • (1992) SIAM J. Optim. , vol.2 , pp. 575-601
    • Mehrotra, S.1
  • 17
    • 0028524565 scopus 로고
    • Polynomiality of infeasible interior point algorithms for linear programming
    • Mizuno, S. (1994), Polynomiality of infeasible interior point algorithms for linear programming, Math. Program., 67 109-119.
    • (1994) Math. Program. , vol.67 , pp. 109-119
    • Mizuno, S.1
  • 18
    • 0011336082 scopus 로고
    • Infeasible-interior-point primal-dual potential reduction algorithms for linear programming
    • Mizuno, S., Kojima, M. and M.J. Todd, (1995), Infeasible-interior-point primal-dual potential reduction algorithms for linear programming, SIAM J. Optim., 5, 52-67.
    • (1995) SIAM J. Optim. , vol.5 , pp. 52-67
    • Mizuno, S.1    Kojima, M.2    Todd, M.J.3
  • 19
    • 0006115292 scopus 로고
    • Applying the progressive hedging algorithm to stochastic generalized networks
    • Mulvey, J.M. and Vladimirous, H. (1991), Applying the progressive hedging algorithm to stochastic generalized networks, Ann. Oper. Res., 31, 399-424.
    • (1991) Ann. Oper. Res. , vol.31 , pp. 399-424
    • Mulvey, J.M.1    Vladimirous, H.2
  • 20
    • 0000514655 scopus 로고
    • Scenarios and policy aggregation in optimization under uncertainty
    • Rockafellar, R.T. and Wets, R.J-B. (1991), Scenarios and policy aggregation in optimization under uncertainty, Math. Oper. Res., 16, 119-147.
    • (1991) Math. Oper. Res. , vol.16 , pp. 119-147
    • Rockafellar, R.T.1    Wets, R.J.-B.2
  • 21
    • 0001060664 scopus 로고
    • Parallel decomposition of multistage stochastic programming problems
    • Ruszczyński, A. (1993), Parallel decomposition of multistage stochastic programming problems, Math. Program. 58 201-228.
    • (1993) Math. Program. , vol.58 , pp. 201-228
    • Ruszczyński, A.1
  • 22
    • 0000365133 scopus 로고    scopus 로고
    • Decomposition methods in stochastic programming
    • Ruszczyński, A. (1997), Decomposition methods in stochastic programming, Math. Program., 79, 333-353.
    • (1997) Math. Program. , vol.79 , pp. 333-353
    • Ruszczyński, A.1
  • 23
    • 0043231094 scopus 로고    scopus 로고
    • Some advances in decomposition methods for stochastic linear programming, stochastic programming
    • State of the art, 1998 (Vancouver, BC)
    • Ruszczyński, A. (1999), Some advances in decomposition methods for stochastic linear programming, Stochastic programming, State of the art, 1998 (Vancouver, BC). Ann. Oper. Res., 85, 153-172.
    • (1999) Ann. Oper. Res. , vol.85 , pp. 153-172
    • Ruszczyński, A.1
  • 24
    • 0013695060 scopus 로고
    • An interior point method for solving a class of linearquadratic stochastic programming problems
    • in: Qi, L. and Womersley, R. (eds.); World Sci. Publishing, River Edge, NJ
    • Sun, J., Wee, K.E. and Zhu, J.S. (1995), An interior point method for solving a class of linearquadratic stochastic programming problems, in: Qi, L. and Womersley, R. (eds.), Recent Advances in Nonsmooth Optimization, World Sci. Publishing, River Edge, NJ, 392-404.
    • (1995) Recent Advances in Nonsmooth Optimization , pp. 392-404
    • Sun, J.1    Wee, K.E.2    Zhu, J.S.3
  • 25
    • 0003058678 scopus 로고
    • An O(√nL)-iteration homogeneous and self-dual linear programming algorithm
    • Ye, Y., Todd, M.J. and Mizuno, S. (1994), An O(√nL)-iteration homogeneous and self-dual linear programming algorithm, Math. Oper. Res., 19, 53-67.
    • (1994) Math. Oper. Res. , vol.19 , pp. 53-67
    • Ye, Y.1    Todd, M.J.2    Mizuno, S.3
  • 26
    • 0041716236 scopus 로고
    • Near boundary behavior of primal-dual potential reduction algorithms for linear programming
    • Ye, Y., Kortanek, K.O., Kaliski, J. and Huang, S. (1993), Near boundary behavior of primal-dual potential reduction algorithms for linear programming, Math. Program., 58, 243-255.
    • (1993) Math. Program. , vol.58 , pp. 243-255
    • Ye, Y.1    Kortanek, K.O.2    Kaliski, J.3    Huang, S.4
  • 27
    • 1542381931 scopus 로고    scopus 로고
    • A primal-dual interior point and decomposition approach to multi-stage stochastic programming
    • (in press); in: Yao, D.D., Zhang, H. and Zhou, H.Y. (eds.); Springer, Berlin
    • Zhang, S. (in press), A primal-dual interior point and decomposition approach to multi-stage stochastic programming, in: Yao, D.D., Zhang, H. and Zhou, H.Y. (eds.), Stochastic Models and Optimization, Springer, Berlin.
    • Stochastic Models and Optimization
    • Zhang, S.1
  • 28
    • 0000252459 scopus 로고
    • On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem
    • Zhang, Y. (1994), On the convergence of a class of infeasible interior-point methods for the horizontal linear complementarity problem, SIAM J. Optim., 4, 208-227.
    • (1994) SIAM J. Optim. , vol.4 , pp. 208-227
    • Zhang, Y.1
  • 29
    • 0011630374 scopus 로고    scopus 로고
    • A lagrangian dual method with self-concordant barrier for multi-stage stochastic convex programming
    • Working Paper, Dept of Mathematics, National University of Singapore; revised 2000
    • Zhao, G.Y. A Lagrangian dual method with self-concordant barrier for multi-stage stochastic convex programming, Working Paper, Dept of Mathematics, National University of Singapore, 1998, revised 2000.
    • (1998)
    • Zhao, G.Y.1
  • 30
    • 0011617062 scopus 로고    scopus 로고
    • A log-barrier method with benders decomposition for solving two-stage stochastic linear programs
    • Zhao, G.Y. (2001), A log-barrier method with Benders decomposition for solving two-stage stochastic linear programs, Math. Program., 90, 507-536.
    • (2001) Math. Program. , vol.90 , pp. 507-536
    • Zhao, G.Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.