메뉴 건너뛰기




Volumn 4, Issue 4, 2007, Pages 313-353

Solving two-stage stochastic programming problems with level decomposition

Author keywords

Decomposition; Stochastic recourse models; Successive approximation

Indexed keywords


EID: 34548178284     PISSN: 1619697X     EISSN: 16196988     Source Type: Journal    
DOI: 10.1007/s10287-006-0026-8     Document Type: Article
Times cited : (55)

References (51)
  • 1
    • 0001614864 scopus 로고    scopus 로고
    • The MOSEK interior-point optimizer for linear programming: An implementation of the homogeneous algorithm
    • In: Frenk H, Roos K, Terlaky T, Zhang S, (eds) Kluwer, Dordrecht
    • Andersen ED, Andersen KD (2000) The MOSEK interior-point optimizer for linear programming: An implementation of the homogeneous algorithm. In: Frenk H, Roos K, Terlaky T, Zhang S, (eds) High performance optimization. Kluwer, Dordrecht, pp 197-232
    • (2000) High Performance Optimization , pp. 197-232
    • Andersen, E.D.1    Andersen, K.D.2
  • 2
    • 0001454852 scopus 로고
    • On minimizing a convex function subject to linear inequalities
    • Beale EML (1955) On minimizing a convex function subject to linear inequalities. J R Stat Soc Ser B 17:173-184
    • (1955) J R Stat Soc Ser B , vol.17 , pp. 173-184
    • Beale, E.M.L.1
  • 3
    • 9644308639 scopus 로고
    • Partitioning procedures for solving mixed-variables programming problems
    • republished in Comput Manage Sci 2:3-19 (2005)
    • Benders JF (1962) Partitioning procedures for solving mixed-variables programming problems. Numer Math 4:238-252 republished in Comput Manage Sci 2:3-19 (2005)
    • (1962) Numer Math , vol.4 , pp. 238-252
    • Benders, J.F.1
  • 5
    • 0022698417 scopus 로고
    • Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse
    • In: Prékopa A, Wets RJ-B (eds)
    • Birge JR, Wets RJ-B (1986) Designing approximation schemes for stochastic optimization problems, in particular for stochastic programs with recourse. In: Prékopa A, Wets RJ-B (eds) Stochastic Programming 84, Vol 1. Mathematical Programming Study 27:54-102
    • (1986) Stochastic Programming 84, Vol 1. Mathematical Programming Study , vol.27 , pp. 54-102
    • Birge, J.R.1    Wets, R.J.-B.2
  • 7
    • 0000813562 scopus 로고
    • Linear programming under uncertainty
    • Dantzig GB (1955) Linear programming under uncertainty. Manage Sci 1:197-206
    • (1955) Manage Sci , vol.1 , pp. 197-206
    • Dantzig, G.B.1
  • 9
    • 0001391104 scopus 로고
    • The decomposition principle for linear programs
    • Dantzig GB, Wolfe P (1960) The decomposition principle for linear programs. Oper Res 8:101-111
    • (1960) Oper Res , vol.8 , pp. 101-111
    • Dantzig, G.B.1    Wolfe, P.2
  • 10
    • 34548178455 scopus 로고    scopus 로고
    • Bundle-type methods for inexact data
    • Csendes T, Rapcsák T (eds)
    • Fábián CI (2000) Csendes T, Rapcsák T (eds) Bundle-type methods for inexact data. Central Eur J Oper Res 8 (special issue); 35-55
    • (2000) Central Eur J Oper Res , vol.8 , Issue.SPEC. ISSUE , pp. 35-55
    • Fábián, C.I.1
  • 11
    • 34548167710 scopus 로고    scopus 로고
    • Decomposing CVaR minimization in two-stage stochastic models
    • Fábián CI (2005) Decomposing CVaR minimization in two-stage stochastic models. Stochastic Programming E-Print Series 20
    • (2005) Stochastic Programming E-Print Series , vol.20
    • Fábián, C.I.1
  • 12
    • 34548170903 scopus 로고    scopus 로고
    • Handling CVaR objectives and constraints in two-stage stochastic models
    • Fábián CI (2006) Handling CVaR objectives and constraints in two-stage stochastic models. RUTCOR Research Report, vol 5
    • (2006) RUTCOR Research Report , vol.5
    • Fábián, C.I.1
  • 13
    • 0041540267 scopus 로고
    • Solving SLP recourse problems with arbitrary multivariate distributions - The dependent case
    • Frauendorfer K (1988) Solving SLP recourse problems with arbitrary multivariate distributions - the dependent case. Math Oper Res 13:377-394
    • (1988) Math Oper Res , vol.13 , pp. 377-394
    • Frauendorfer, K.1
  • 14
    • 0023844906 scopus 로고
    • A solution method for SLP recourse problems with arbitrary distributions - The independent case
    • Frauendorfer K, Kall P (1988) A solution method for SLP recourse problems with arbitrary distributions - The independent case. Probl Control Inf Theory 17:177-205
    • (1988) Probl Control Inf Theory , vol.17 , pp. 177-205
    • Frauendorfer, K.1    Kall, P.2
  • 15
    • 21344456261 scopus 로고    scopus 로고
    • Solving linear programs with multiple right-hand sides: Pricing and ordering schemes
    • Gassmann HI, Wallace SW (1996) Solving linear programs with multiple right-hand sides: Pricing and ordering schemes. Ann Oper Res 64:237-259
    • (1996) Ann Oper Res , vol.64 , pp. 237-259
    • Gassmann, H.I.1    Wallace, S.W.2
  • 16
    • 0042659381 scopus 로고    scopus 로고
    • Reoptimization with the primal-dual interior point method
    • Gondzio J, Grothey A (2003) Reoptimization with the primal-dual interior point method. SIAM J Optim 13:842-864
    • (2003) SIAM J Optim , vol.13 , pp. 842-864
    • Gondzio, J.1    Grothey, A.2
  • 17
    • 84933801768 scopus 로고
    • Solving complete fixed recourse problems by successive discretization
    • In: Kall P, Prékopa A (eds) Springer, Berlin, Heidelberg New York
    • Kall P (1980) Solving complete fixed recourse problems by successive discretization. In: Kall P, Prékopa A (eds) Recent Results in Stochastic Programming, Lecture Notes in Economics and Math. Systems 170. Springer, Berlin, Heidelberg New York, pp 135-138
    • (1980) Recent Results in Stochastic Programming, Lecture Notes in Economics and Math. Systems , vol.170 , pp. 135-138
    • Kall, P.1
  • 19
    • 0004914713 scopus 로고
    • Solving stochastic programming problems with recourse including error bounds
    • Kall P, Stoyan D (1982) Solving stochastic programming problems with recourse including error bounds. Math Opernforsch Stat Ser Optim 13:431-447
    • (1982) Math Opernforsch Stat Ser Optim , vol.13 , pp. 431-447
    • Kall, P.1    Stoyan, D.2
  • 22
    • 34548171886 scopus 로고
    • On the ellipsoid method
    • Klafszky E, Terlaky T (1992) On the ellipsoid method. Radov Mat 8:269-280
    • (1992) Radov Mat , vol.8 , pp. 269-280
    • Klafszky, E.1    Terlaky, T.2
  • 23
    • 0040730852 scopus 로고
    • Duality in stochastic linear and dynamic programming
    • Springer, Berlin Heidelberg New York
    • Klein Haneveld WK (1986) Duality in stochastic linear and dynamic programming. Lecture Notes in Economics and Mathematical Systems, vol 274. Springer, Berlin Heidelberg New York
    • (1986) Lecture Notes in Economics and Mathematical Systems , vol.274
    • Klein Haneveld, W.K.1
  • 24
    • 29444435741 scopus 로고    scopus 로고
    • Computational aspects of minimizing conditional value-at-risk
    • Künzi-Bay A, Mayer J (2006) Computational aspects of minimizing conditional value-at-risk. Comput Manage Sci 3:3-27
    • (2006) Comput Manage Sci , vol.3 , pp. 3-27
    • Künzi-Bay, A.1    Mayer, J.2
  • 25
    • 34548168768 scopus 로고
    • Basic theory in nondifferentiable optimization
    • Research Report No. 181, Institut National de Recherche en Informatique at en Automatique, Domaine de Voluceau, Rocquencourt, France
    • Lemaréchal C (1982) Basic theory in nondifferentiable optimization. Research Report No. 181, Institut National de Recherche en Informatique at en Automatique, Domaine de Voluceau, Rocquencourt, France
    • (1982)
    • Lemaréchal, C.1
  • 27
    • 0742324304 scopus 로고    scopus 로고
    • The empirical behavior of sampling methods for stochastic programming
    • Optimization Technical Report 02-01. Computer Science Department, University of Wisconsin-Madison
    • Linderoth JT, Shapiro A, Wright SJ (2002) The empirical behavior of sampling methods for stochastic programming. Optimization Technical Report 02-01. Computer Science Department, University of Wisconsin-Madison
    • (2002)
    • Linderoth, J.T.1    Shapiro, A.2    Wright, S.J.3
  • 28
    • 0032632474 scopus 로고    scopus 로고
    • Monte Carlo bounding techniques for determining solution quality in stochastic programs
    • Mak W-K, Morton D, Wood RK (1999) Monte Carlo bounding techniques for determining solution quality in stochastic programs. Oper Res Lett 24:47-56
    • (1999) Oper Res Lett , vol.24 , pp. 47-56
    • Mak, W.-K.1    Morton, D.2    Wood, R.K.3
  • 29
    • 0038559895 scopus 로고    scopus 로고
    • A generalized dual phase-2 simplex algorithm
    • Maros I (2003a) A generalized dual phase-2 simplex algorithm. Eur J Oper Res 149:1-16
    • (2003) Eur J Oper Res , vol.149 , pp. 1-16
    • Maros, I.1
  • 32
    • 0000937493 scopus 로고
    • A new scenario decomposition method for large scale stochastic optimization
    • Mulvey JM, Ruszczyński A (1995) A new scenario decomposition method for large scale stochastic optimization. Oper Res 43:477-490
    • (1995) Oper Res , vol.43 , pp. 477-490
    • Mulvey, J.M.1    Ruszczyński, A.2
  • 33
    • 0001454014 scopus 로고    scopus 로고
    • A branch and bound method for stochastic global optimization
    • Norkin VI, Pflug GCh, Ruszczyński A (1998) A branch and bound method for stochastic global optimization. Math program 83:425-450
    • (1998) Math Program , vol.83 , pp. 425-450
    • Norkin, V.I.1    Pflug, G.Ch.2    Ruszczyński, A.3
  • 34
    • 0002783594 scopus 로고
    • Logarithmic concave measures with applications to stochastic programming
    • Prékopa A (1971) Logarithmic concave measures with applications to stochastic programming. Acta Sci Math (Szeged) 32:301-316
    • (1971) Acta Sci Math (Szeged) , vol.32 , pp. 301-316
    • Prékopa, A.1
  • 35
    • 0000678433 scopus 로고
    • Contributions to the theory of stochastic programming
    • Prékopa A (1973) Contributions to the theory of stochastic programming. Math Program 4:202-221
    • (1973) Math Program , vol.4 , pp. 202-221
    • Prékopa, A.1
  • 38
    • 0002062038 scopus 로고    scopus 로고
    • Optimization of conditional value-at-risk
    • Rockafellar RT, Uryasev S (2000) Optimization of conditional value-at-risk. J Risk 2:21-41
    • (2000) J Risk , vol.2 , pp. 21-41
    • Rockafellar, R.T.1    Uryasev, S.2
  • 40
    • 0022751475 scopus 로고
    • A regularized decomposition method for minimizing the sum of polyhedral functions
    • Ruszczyński A (1986) A regularized decomposition method for minimizing the sum of polyhedral functions. Math Program 35:309-333
    • (1986) Math Program , vol.35 , pp. 309-333
    • Ruszczyński, A.1
  • 43
    • 0031222339 scopus 로고    scopus 로고
    • Accelerating the regularized decomposition method for two-stage stochastic linear problems
    • Ruszczyński A, Áwietanowski A (1997) Accelerating the regularized decomposition method for two-stage stochastic linear problems. Eur J Oper Res 101:328-342
    • (1997) Eur J Oper Res , vol.101 , pp. 328-342
    • Ruszczyński, A.1    Áwietanowski, A.2
  • 46
    • 0001762682 scopus 로고    scopus 로고
    • A simulation-based approach to two-stage stochastic programming with recourse
    • Shapiro A, Homem-de-Mello T (1998) A simulation-based approach to two-stage stochastic programming with recourse. Math Program 81:301-325
    • (1998) Math Program , vol.81 , pp. 301-325
    • Shapiro, A.1    Homem-de-Mello, T.2
  • 47
    • 0034550507 scopus 로고    scopus 로고
    • On the rate of convergence of Monte Carlo approximations of stochastic programs
    • Shapiro A, Homem-de-Mello T (2000) On the rate of convergence of Monte Carlo approximations of stochastic programs. SIAM J Optim 11:70-86
    • (2000) SIAM J Optim , vol.11 , pp. 70-86
    • Shapiro, A.1    Homem-de-Mello, T.2
  • 48
    • 0001857581 scopus 로고
    • A computer code for the solution of probabilistic-constrained stochastic programming problems
    • In: Ermoliev Yu, Wets RJ-B (eds) Springer, Berlin Heidelberg New York
    • Szántai T (1988) A computer code for the solution of probabilistic-constrained stochastic programming problems. In: Ermoliev Yu, Wets RJ-B (eds) Numerical Techniques for Stochastic Optimization. Springer, Berlin Heidelberg New York
    • (1988) Numerical Techniques for Stochastic Optimization
    • Szántai, T.1
  • 49
    • 0014534894 scopus 로고
    • L-Shaped linear programs with applications to optimal control and stochastic programming
    • Van Slyke R, Wets RJ-B (1969) L-Shaped linear programs with applications to optimal control and stochastic programming. SIAM J Appl Math 17:638-663
    • (1969) SIAM J Appl Math , vol.17 , pp. 638-663
    • Van Slyke, R.1    Wets, R.J.-B.2
  • 50
    • 0016084468 scopus 로고
    • Stochastic programs with fixed recourse: The equivalent deterministic program
    • Wets RJ-B (1974) Stochastic programs with fixed recourse: The equivalent deterministic program. SIAM Review 16:309-339
    • (1974) SIAM Review , vol.16 , pp. 309-339
    • Wets, R.J.-B.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.